Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 23 Jan 2006
Posts: 191

If n is positive, which of the following is equal to
[#permalink]
Show Tags
Updated on: 16 Apr 2012, 02:05
Question Stats:
71% (00:49) correct 29% (01:20) wrong based on 1007 sessions
HideShow timer Statistics
If n is positive, which of the following is equal to \(\frac{1}{\sqrt{n+1}\sqrt{n}}\) A. 1 B. \(\sqrt{2n+1}\) C. \(\frac{\sqrt{n+1}}{\sqrt{n}}\) D. \(\sqrt{n+1}\sqrt{n}\) E. \(\sqrt{n+1}+\sqrt{n}\)
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by kook44 on 28 Jun 2006, 06:36.
Last edited by Bunuel on 16 Apr 2012, 02:05, edited 1 time in total.
Edited the question and added the OA




Math Expert
Joined: 02 Sep 2009
Posts: 49251

If n is positive, which of the following is equal to
[#permalink]
Show Tags
16 Apr 2012, 02:19
If n is positive, which of the following is equal to \(\frac{1}{\sqrt{n+1}\sqrt{n}}\)A. 1 B. \(\sqrt{2n+1}\) C. \(\frac{\sqrt{n+1}}{\sqrt{n}}\) D. \(\sqrt{n+1}\sqrt{n}\) E. \(\sqrt{n+1}+\sqrt{n}\) This question is dealing with rationalisation of a fraction. Rationalisation is performed to eliminate irrational expression in the denominator. For this particular case we can do this by applying the following rule: \((ab)(a+b)=a^2b^2\). Multiple both numerator and denominator by \(\sqrt{n+1}+\sqrt{n}\): \(\frac{\sqrt{n+1}+\sqrt{n}}{(\sqrt{n+1}\sqrt{n})(\sqrt{n+1}+\sqrt{n})}=\frac{\sqrt{n+1}+\sqrt{n}}{(\sqrt{n+1})^2(\sqrt{n})^2)}=\frac{\sqrt{n+1}+\sqrt{n}}{n+1n}=\sqrt{n+1}+\sqrt{n}\). Answer: E.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Intern
Joined: 06 Apr 2012
Posts: 31

Re: fraction
[#permalink]
Show Tags
Updated on: 18 Nov 2012, 03:47
Quote: If n is positive, which of the following is equal to \(\frac{1}{\sqrt{n+1}\sqrt{n}}\)
A. 1
B. \(\sqrt{2n+1}\)
C. \(\frac{\sqrt{n+1}}{\sqrt{n}}\)
D. \(\sqrt{n+1}\sqrt{n}\)
E. \(\sqrt{n+1}+\sqrt{n}\)
This question is dealing with rationalisation of a fraction. Rationalisation is performed to eliminate irrational expression in the denominator. For this particular case we can do this by applying the following rule: \((ab)(a+b)=a^2b^2\).
Multiple both numerator and denominator by \(\sqrt{n+1}+\sqrt{n}\): \(\frac{\sqrt{n+1}+\sqrt{n}}{(\sqrt{n+1}\sqrt{n})(\sqrt{n+1}+\sqrt{n})}=\frac{\sqrt{n+1}+\sqrt{n}}{(\sqrt{n+1})^2(\sqrt{n})^2)}=\frac{\sqrt{n+1}+\sqrt{n}}{n+1n}=\sqrt{n+1}+\sqrt{n}\).
Answer: E. Bunuel  just wanted to clarify an aspect of the roots  the final answer of this problem is E and it is perfectly understood. However, if I want to simplify the \(\sqrt{n+1} + \sqrt{n}\) even more... theoretically I could "unroot" these expressions, so that I get \(2n+1\), however, as the answer B is clearly wrong (and I can see why), I want to but I struggle to understand how to "put the roots back" in the \(2n+1\) to get an equivalent of \(\sqrt{n+1} + \sqrt{n}\). Any thoughts on this matter? Thanks!
Originally posted by kalita on 17 Nov 2012, 05:42.
Last edited by kalita on 18 Nov 2012, 03:47, edited 2 times in total.



Math Expert
Joined: 02 Sep 2009
Posts: 49251

Re: fraction
[#permalink]
Show Tags
17 Nov 2012, 05:51
ikokurin wrote: Bu nuel wrote: If n is positive, which of the following is equal to \(\frac{1}{\sqrt{n+1}\sqrt{n}}\)
A. 1
B. \(\sqrt{2n+1}\)
C. \(\frac{\sqrt{n+1}}{\sqrt{n}}\)
D. \(\sqrt{n+1}\sqrt{n}\)
E. \(\sqrt{n+1}+\sqrt{n}\)
This question is dealing with rationalisation of a fraction. Rationalisation is performed to eliminate irrational expression in the denominator. For this particular case we can do this by applying the following rule: \((ab)(a+b)=a^2b^2\).
Multiple both numerator and denominator by \(\sqrt{n+1}+\sqrt{n}\): \(\frac{\sqrt{n+1}+\sqrt{n}}{(\sqrt{n+1}\sqrt{n})(\sqrt{n+1}+\sqrt{n})}=\frac{\sqrt{n+1}+\sqrt{n}}{(\sqrt{n+1})^2(\sqrt{n})^2)}=\frac{\sqrt{n+1}+\sqrt{n}}{n+1n}=\sqrt{n+1}+\sqrt{n}\).
Answer: E. Bunuel  just wanted to clarify an aspect of the roots  the final answer of this problem is E and it is perfectly understood. However, if I want to simplify the SQRT(n+1) + SQRT(n) even more... theoretically I could "unsquare" these expressions, so that I get 2n+1, however, as the answer B is clearly wrong (and I can see why), I struggle to understand how to "square back" the 2n+1 to get an equivalent of SQRT(n+1) + SQRT(n). Can you help me out or share your thoughts on the matter? Thanks! I don't understand what you mean: how can you get \(2n+1\) from \(\sqrt{n+1}+\sqrt{n}\)?
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 06 Apr 2012
Posts: 31

Re: fraction
[#permalink]
Show Tags
Updated on: 18 Nov 2012, 03:39
Quote: I don't understand what you mean: how can you get \(2n+1\) from \(\sqrt{n+1}+\sqrt{n}\)? I meant some people might get \(\sqrt{2n+1}\) which is the answer B. However, I can see why \(\sqrt{n+1}+\sqrt{n}\) is NOT equal \(\sqrt{2n+1}\) even though it might be tempting to simplify it to this form (and pick the wrong answer). But my question is can we simplify \(\sqrt{n+1}+\sqrt{n}\) further by "squaring" both terms and then "unsquaring" them/the expression back somehow... or what could be an equivalent of \(\sqrt{n+1}+\sqrt{n}\)?
Originally posted by kalita on 17 Nov 2012, 06:06.
Last edited by kalita on 18 Nov 2012, 03:39, edited 1 time in total.



Math Expert
Joined: 02 Sep 2009
Posts: 49251

Re: fraction
[#permalink]
Show Tags
17 Nov 2012, 06:19
ikokurin wrote: I meant some people might get SQRT(2n+1) which is the answer B. However, I can see why SQRT(n+1) + SQRT(n) is NOT equal SQRT(2n+1) even though it might be tempting to simplify it to this form (and pick the wrong answer). But my question is can we simplify SQRT(n+1) + SQRT(n) further by "squaring" both terms and then "squarerooting" them again somehow... or what could be an equivalent of SQRT(n+1) + SQRT(n)? \(\sqrt{n+1}+\sqrt{n}\) is the simplest form. If you square it you'll get \((\sqrt{n+1}+\sqrt{n})^2=(\sqrt{n+1})^2+2\sqrt{n+1}*\sqrt{n}+\sqrt{n}^2=2n+1+2\sqrt{(n+1)n}\). You cannot take square root from this expression to get anything better than \(\sqrt{n+1}+\sqrt{n}\). Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 06 Apr 2012
Posts: 31

Re: fraction
[#permalink]
Show Tags
Updated on: 18 Nov 2012, 03:32
Quote: \(\sqrt{n+1}+\sqrt{n}\) is the simplest form. If you square it you'll get \((\sqrt{n+1}+\sqrt{n})^2=(\sqrt{n+1})^2+2\sqrt{n+1}*\sqrt{n}+\sqrt{n}^2=2n+1+2\sqrt{(n+1)n}\). You cannot take square root from this expression to get anything better than \(\sqrt{n+1}+\sqrt{n}\).
Hope it's clear. I see. What you are saying is clear but your answer does not exactly address what I am after. I can see that \((\sqrt{n+1}+\sqrt{n})^2\) only complicates it further. Sorry to be pertinacious on this  if we do \((\sqrt{n+1})^2+(\sqrt{n})^2\) => we will get \(n+1 + n = 2n + 1\) => can we "undo" the expression \(2n + 1\) somehow to get the equivalent of \(\sqrt{n+1}+\sqrt{n}\)? I promise this is the last one:) P.S. Also, please let me know if it would be better to send a PM on related "clarifying" questions...
Originally posted by kalita on 17 Nov 2012, 06:37.
Last edited by kalita on 18 Nov 2012, 03:32, edited 1 time in total.



Math Expert
Joined: 02 Sep 2009
Posts: 49251

Re: fraction
[#permalink]
Show Tags
17 Nov 2012, 06:45
ikokurin wrote: \(\sqrt{n+1}+\sqrt{n}\) is the simplest form. If you square it you'll get \((\sqrt{n+1}+\sqrt{n})^2=(\sqrt{n+1})^2+2\sqrt{n+1}*\sqrt{n}+\sqrt{n}^2=2n+1+2\sqrt{(n+1)n}\). You cannot take square root from this expression to get anything better than \(\sqrt{n+1}+\sqrt{n}\).
Hope it's clear. I see. What you are saying is clear but your answer does not exactly address what I am after. Sorry to be pertinacious on this but I was wondering if we can do (SQRT(n+1))^2 + (SQRT(n))^2 => we will get n+1 + n = 2n + 1 => can we "undo" the expression 2n + 1 somehow to get the equivalent of SQRT(n+1) + SQRT(n)? I promise this is the last one:) Also, please let me know if it would be better to send a PM on related "clarifying" questions...[/quote] The answer is no, these expressions are not equal. P.S. Please use formatting, check here: rulesforpostingpleasereadthisbeforeposting133935.html#p1096628
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 06 Apr 2012
Posts: 31

Re: fraction
[#permalink]
Show Tags
17 Nov 2012, 18:44
Quote: The answer is no, these expressions are not equal. P.S. Please use formatting, check here: rulesforpostingpleasereadthisbeforeposting133935.html#p1096628I understand they are not equal, thanks for help. So I take away there is no way to go from \(2n+1\) (obtained after squaring both terms (\((\sqrt{n+1})^2 + (\sqrt{n})^2\)) into something else that could be an equivalent of\(\sqrt{n+1} + \sqrt{n}\). As mentioned above, for those having issues with exponents/roots, it is possible to make a mistake of simplifying \((\sqrt{n+1})^2 + (\sqrt{n})^2\) into \(\sqrt{2n+1}\) (which is incorrect); nevertheless I wanted to see if there was a way to do something about \(2n+1\) to make it equal to \(\sqrt{n+1} + \sqrt{n}\). For some reason, having inner desire to combine those \(n\) terms to make it all look nicer, it bugs me that leaving the answer as \(\sqrt{n+1} + \sqrt{n}\) is all we can do about this equation; especially after I saw some tricks/solutions relating to the tricky exponent problems and how one can do "wonders" with squaring and unsquaring things I was thinking about simplifying this thing into something like, obviously grossly exaggerated, \(^4\sqrt{2n+1}\) or \(\sqrt{2n}+\sqrt{1}\), etc., by "squarerooting" \(2n+1\) back somehow. But again I know the previous examples are plain wrong, just giving an example of what one can go through working through possibilities. Anyhow, enough of this rumble, let me know if you have anything to add...and thanks much for patience. Regards,



Senior Manager
Joined: 13 Aug 2012
Posts: 436
Concentration: Marketing, Finance
GPA: 3.23

Re: If n is positive, which of the following is equal to
[#permalink]
Show Tags
11 Dec 2012, 04:33
\(\frac{1}{\sqrt{n+1}\sqrt{n}}\) \(\frac{1}{\sqrt{n+1}\sqrt{n}} * \frac{\sqrt{n+1}+\sqrt{n}}{\sqrt{n+1}+\sqrt{n}}\) \(\frac{\sqrt{n+1}+\sqrt{n}}{n+1n}\) \(\frac{\sqrt{n+1}+\sqrt{n}}{1}\) Answer: E
_________________
Impossible is nothing to God.



Intern
Joined: 03 Jan 2013
Posts: 15

Re: If n is positive, which of the following is equal to
[#permalink]
Show Tags
23 Jan 2013, 08:27
I have a quick question on this ..when the initial fraction was rationalized you used:
\(\sqrt{n+1}+ \sqrt{n} / \sqrt{n+1}+ \sqrt{n}\)
did you change the sign from negative to positive since the question stated "n" is a positive number. Wouldn't you have to use the same denominator when Rationalizing a fraction?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8281
Location: Pune, India

Re: If n is positive, which of the following is equal to
[#permalink]
Show Tags
23 Jan 2013, 20:23
pharm wrote: I have a quick question on this ..when the initial fraction was rationalized you used:
\(\sqrt{n+1}+ \sqrt{n} / \sqrt{n+1}+ \sqrt{n}\)
did you change the sign from negative to positive since the question stated "n" is a positive number. Wouldn't you have to use the same denominator when Rationalizing a fraction? When there is an irrational number in the denominator, you rationalize it by multiplying it with its complement i.e. if it is \(\sqrt{a} + \sqrt{b}\) in the denominator, you will multiply by \(\sqrt{a}  \sqrt{b}\). This is done to use the algebraic identity (a + b)(a  b) = a^2  b^2. When a and b are irrational, a^2 and b^2 become rational (given we are dealing with only square roots) To keep the fraction same, you need to multiply the numerator with the same number as well. An example will make it clear: Rationalize \(\frac{3}{{\sqrt{2}  1}}\) = \(\frac{3}{{\sqrt{2}  1}} * \frac{\sqrt{2} + 1}{\sqrt{2} + 1}\) = \(\frac{3*(\sqrt{2} + 1)}{(\sqrt{2})^2  1^2}\) = \(\frac{3*(\sqrt{2} + 1)}{2  1}\) The denominator has become rational. Similarly, if the denominator has \(\sqrt{a}  \sqrt{b}\), you will multiply by \(\sqrt{a} + \sqrt{b}\). In this question too, you can substitute n = 1. The given expression becomes \(\frac{1}{{\sqrt{2}  1}}\) Rationalize it and you will get \(\sqrt{2} + 1\). Put n = 1 in the options. Only option (E) gives you \(\sqrt{2} + 1\).
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Joined: 03 Jan 2013
Posts: 15

Re: If n is positive, which of the following is equal to
[#permalink]
Show Tags
28 Jan 2013, 08:51
Thanks Karishma that cleared things up



SVP
Joined: 06 Sep 2013
Posts: 1820
Concentration: Finance

Re: If n is positive, which of the following is equal to
[#permalink]
Show Tags
22 Nov 2013, 07:12
kook44 wrote: If n is positive, which of the following is equal to \(\frac{1}{\sqrt{n+1}\sqrt{n}}\)
A. 1
B. \(\sqrt{2n+1}\)
C. \(\frac{\sqrt{n+1}}{\sqrt{n}}\)
D. \(\sqrt{n+1}\sqrt{n}\)
E. \(\sqrt{n+1}+\sqrt{n}\) Isn't it much easier to just pick n=1 and then look for target in answer choices? Cheers! J



Manager
Joined: 25 Oct 2013
Posts: 154

Re: If n is positive, which of the following is equal to
[#permalink]
Show Tags
22 Nov 2013, 08:01
jlgdr wrote: kook44 wrote: If n is positive, which of the following is equal to \(\frac{1}{\sqrt{n+1}\sqrt{n}}\)
A. 1
B. \(\sqrt{2n+1}\)
C. \(\frac{\sqrt{n+1}}{\sqrt{n}}\)
D. \(\sqrt{n+1}\sqrt{n}\)
E. \(\sqrt{n+1}+\sqrt{n}\) Isn't it much easier to just pick n=1 and then look for target in answer choices? Cheers! J What if more than one answer choice gives you same value? first, we have to try original expression with 1 and try each of the choices with 1. If we are lucky we have only one choice matching. but what if there are 2 or even 3 answer choices? we would then have to pick another number. Personally I feel solving it is faster in this case. Sometimes number picking works faster. knowing when to use number picking is the difficult part.
_________________
Click on Kudos if you liked the post!
Practice makes Perfect.



SVP
Joined: 06 Sep 2013
Posts: 1820
Concentration: Finance

Re: If n is positive, which of the following is equal to
[#permalink]
Show Tags
22 Nov 2013, 08:29
Ya I guess your right after solving the way Bunuel did it took less than 20 secs
Posted from my mobile device



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8281
Location: Pune, India

Re: If n is positive, which of the following is equal to
[#permalink]
Show Tags
24 Nov 2013, 21:05
jlgdr wrote: kook44 wrote: If n is positive, which of the following is equal to \(\frac{1}{\sqrt{n+1}\sqrt{n}}\)
A. 1
B. \(\sqrt{2n+1}\)
C. \(\frac{\sqrt{n+1}}{\sqrt{n}}\)
D. \(\sqrt{n+1}\sqrt{n}\)
E. \(\sqrt{n+1}+\sqrt{n}\) Isn't it much easier to just pick n=1 and then look for target in answer choices? Cheers! J Yes, absolutely it is. I would answer this question by plugging in the values but you have to be careful of two things. When pluggin in values in the options, two or more options might seem to satisfy. If this happens, you need to plug in a different number in those two to get the actual correct answer. Also, you need to ensure that the value given by option actually does not match the required value before discarding it. e.g. here if I put n = 1, \(\frac{1}{\sqrt{n+1}\sqrt{n}}\) = \(\frac{1}{\sqrt{2}1}\) while option (E) gives \(\sqrt{n+1}+\sqrt{n}\) = \(\sqrt{2}+1\) You cannot discard option (E) because it doesn't look the same. You must rationalize the value obtained from the expression and then compare it with what you get from option (E). So you must be careful.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Joined: 22 Jan 2018
Posts: 5

Re: If n is positive, which of the following is equal to
[#permalink]
Show Tags
30 Jan 2018, 01:47
Bunuel wrote: If n is positive, which of the following is equal to \(\frac{1}{\sqrt{n+1}\sqrt{n}}\)
A. 1
B. \(\sqrt{2n+1}\)
C. \(\frac{\sqrt{n+1}}{\sqrt{n}}\)
D. \(\sqrt{n+1}\sqrt{n}\)
E. \(\sqrt{n+1}+\sqrt{n}\)
This question is dealing with rationalisation of a fraction. Rationalisation is performed to eliminate irrational expression in the denominator. For this particular case we can do this by applying the following rule: \((ab)(a+b)=a^2b^2\).
Multiple both numerator and denominator by \(\sqrt{n+1}+\sqrt{n}\): \(\frac{\sqrt{n+1}+\sqrt{n}}{(\sqrt{n+1}\sqrt{n})(\sqrt{n+1}+\sqrt{n})}=\frac{\sqrt{n+1}+\sqrt{n}}{(\sqrt{n+1})^2(\sqrt{n})^2)}=\frac{\sqrt{n+1}+\sqrt{n}}{n+1n}=\sqrt{n+1}+\sqrt{n}\).
Answer: E. Hi! I do not understand, how you came up with the last part of the solution where you just simplify and take the expression from the denominator away. thank you!



Math Expert
Joined: 02 Sep 2009
Posts: 49251

Re: If n is positive, which of the following is equal to
[#permalink]
Show Tags
30 Jan 2018, 02:34
Jannnn04 wrote: Bunuel wrote: If n is positive, which of the following is equal to \(\frac{1}{\sqrt{n+1}\sqrt{n}}\)
A. 1
B. \(\sqrt{2n+1}\)
C. \(\frac{\sqrt{n+1}}{\sqrt{n}}\)
D. \(\sqrt{n+1}\sqrt{n}\)
E. \(\sqrt{n+1}+\sqrt{n}\)
This question is dealing with rationalisation of a fraction. Rationalisation is performed to eliminate irrational expression in the denominator. For this particular case we can do this by applying the following rule: \((ab)(a+b)=a^2b^2\).
Multiple both numerator and denominator by \(\sqrt{n+1}+\sqrt{n}\): \(\frac{\sqrt{n+1}+\sqrt{n}}{(\sqrt{n+1}\sqrt{n})(\sqrt{n+1}+\sqrt{n})}=\frac{\sqrt{n+1}+\sqrt{n}}{(\sqrt{n+1})^2(\sqrt{n})^2)}=\frac{\sqrt{n+1}+\sqrt{n}}{n+1n}=\sqrt{n+1}+\sqrt{n}\).
Answer: E. Hi! I do not understand, how you came up with the last part of the solution where you just simplify and take the expression from the denominator away. thank you! The denominator is n+1n, which is 1: n + 1  n= 1.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Director
Joined: 09 Mar 2016
Posts: 859

Re: If n is positive, which of the following is equal to
[#permalink]
Show Tags
25 Mar 2018, 06:15
kook44 wrote: If n is positive, which of the following is equal to \(\frac{1}{\sqrt{n+1}\sqrt{n}}\)
A. 1
B. \(\sqrt{2n+1}\)
C. \(\frac{\sqrt{n+1}}{\sqrt{n}}\)
D. \(\sqrt{n+1}\sqrt{n}\)
E. \(\sqrt{n+1}+\sqrt{n}\) this link is great source about rationalizing denominator http://www.wtamu.edu/academic/anns/mps/ ... nalize.htm
_________________
In English I speak with a dictionary, and with people I am shy.




Re: If n is positive, which of the following is equal to &nbs
[#permalink]
25 Mar 2018, 06:15



Go to page
1 2
Next
[ 21 posts ]



