Root of (16*20+8*32)=

Question

\sqrt{16*20+8*32}=

(A)  4\sqrt{20} 
(B) 24
(C) 25
(D)  4\sqrt{20}+8\sqrt{2} 
(E) 32

Bunuel · Accepted Answer

SOLUTION

\sqrt{16*20+8*32}=

(A)  4\sqrt{20} 
(B) 24
(C) 25
(D)  4\sqrt{20}+8\sqrt{2} 
(E) 32

Factor out 16:  \sqrt{16*20+8*32}=\sqrt{16(20+8*2)}=\sqrt{16*36}=4*6=24 .

Answer: B.

Bunuel · Answer

It should be:

\sqrt{16*20+8*32}=\sqrt{2^4*2^2*5+2^3*2^5}=\sqrt{2^6*5+2^8}=\sqrt{2^6(5+2^2)}=\sqrt{2^6*9}=2^3*3=24 .

Hope it's clear.

dexerash · Answer

\sqrt{4*4*4*5 + 4*4*4*4} = 2*2*2\sqrt{5+4} = 8*\sqrt{9} = 8*3 = 24

B

asveaass · Answer

Obviously I don't get this..... :shock:

I know this must be wrong since no answer choice allows this, but where am I mistaking? Appreciate the help! Rt (16*20)+(8*32)= Rt(2^4*2^2*5)+(2^3*2^5)= 2^3 Rt(5)+2^4= 8Rt5+16 ??

healthjunkie · Answer

why can't you factor out a 4? it doesnt work when I do it.

EMPOWERgmatRichC · Answer

Hi soniasawhney,

You CAN factor out a 4, but I'd like to see your work so that we can assess whether you're factoring out that 4 correctly or not. So, can you post your work/"steps"?

As an aside, after factoring out a 4, you'd then have more work to do to get to the solution.

GMAT assassins aren't born, they're made,
Rich

healthjunkie · Answer

This is how I was doing it..

4 
4 
4 
take the square root...
(2)(6)=12

However, I now realize that the way I was factoring it, I actually was taking out 'too many' 4's and I should have done it like so...is this right? 
4 
4 
4 
take the square root...
2*12=24

Let me know if that makes sense!

EMPOWERgmatRichC · Answer

Hi soniasawhney,

As you've come to realize, you have to be careful when factoring out numbers from large calculations.

There are actually several different ways to 'factor down' and simplify this question, but your second approach is correct (and is just as valid as any other).

Here's another way to do it (based on the same ideas that you were using):

You might catch that 16 is a factor of BOTH terms (16x20 and 8x32). By factoring out 16, we can simplify the calculation even further....

Root

Root 
Root ]
Root ]

4(6) = 24

GMAT assassins aren't born, they're made,
Rich

faizanswx · Answer

why is 16 only factored from 2 and the 20 and 8 are left alone? sorry if this is a bad question, I'm new to the gmat and need every explanation i could get

EMPOWERgmatRichC · Answer

Hi faizanswx,

When dealing with radicals, you should look for 'perfect squares' (re: 4, 9, 16, 25, etc.) that you can factor-out of the radical...

eg. √50 = √(25x2) = 5√2

In the given prompt, 16 can be factored-out (it becomes '4') and then the 36 can factored-out (it becomes '6').

GMAT assassins aren't born, they're made,
Rich

EricImasogie · Answer

Ok, this problem is completely baffling the crap out of me! lol!!

Let me first state an assumption I made when doing this problem:

Step 1: Sqrt  = sqrt(16*20) + sqrt(8*32)

Step 2: Sqrt (16*20) = 4*Sqrt(20) = is atleast 16 & sqrt(8*32) = 16

So how in the world is this answer not atleast 32 (I know 32 is not in the answer choice) ? or did I make a big mistake in step 1?

Bunuel · Answer

You should brush-up fundamentals before attempting the questions. Generally \sqrt{a+b} eq \sqrt{a} + \sqrt{b} . For example, (\sqrt{4+4}=\sqrt{8}) eq (\sqrt{4} + \sqrt{4}=4) . Theory on Exponents: math-number-theory-88376.html Tips on Exponents: exponents-and-roots-on-the-gmat-tips-and-hints-174993.html All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39 All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60 Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

EMPOWERgmatRichC · Answer

Hi EricImasogie,

While the major Radical rules won't show up too often on Test Day (you'll likely see just 1-2 questions that will involve radical rules), they are a standard part of the GMAT, so if you know the rules, then you should be able to pick up these points.

Since your 'assumptions' about how the math 'worked' were incorrect, I have a few questions about your studies so far:

1) How long have you been studying?
2) What resources have you been using?

It might be that you need some general 'math' practice before you do too much more GMAT practice.

GMAT assassins aren't born, they're made,
Rich

mcelroytutoring · Answer

Here is a visual that should help.

ScottTargetTestPrep · Answer

Solution:

We must first simplify the expression in the square root before actually taking the square root. In other words, we have to get the product of 16 and 20 and add it to the product of 8 and 32 before taking the square root.

√

√(320 + 256)

√576 = 24

The answer is B.

Note: If struggling with determining the value of √576, we could have used the answer choices to our advantage. We need to ask ourselves what number, when squared, equals 576. Since we should have the value of 25^2 memorized, we would know that 25^2 = 625. Since 576 is slightly less than 625, we can reasonably determine that 24^2 = 576.

OptimusPrepJanielle · Answer

The first thing when you see such questions should be to simplify 
16*20 + 8*32 = 320 + 256 = 576 
Now,  \sqrt{576} = 24

Correct Option: B

Abhishek009 · Answer

\sqrt{16*20+8*32}

=  \sqrt{320+256}

=  \sqrt{576}

24 * 24 = 576  , Hence Answer must be (B)

Thib33600 · Answer

so whenever we have an exponent inside a square root, we didvide by 2? 
eg: square root of 2^8 gives 2^4?
square root of  4^6 gives 4^3?

Bunuel · Answer

Yes, the square root of a number,  \sqrt{x} , means  x^{\frac{1}{2}} , and thus essentially says to multiply the exponent of x by 1/2. Similarly,  \sqrt {x}  means  x^{\frac{1}{3}} , and thus essentially says to multiply the exponent of x by 1/3. And so on.

8. Exponents and Roots of Numbers 
 
   Theory  
 Exponents and Roots on the GMAT: Tips and hints 
 Cyclicity and the remainders on the GMAT 
 
   Questions  
 Units digits, exponents, remainders problems 
 Tough and tricky DS exponents and roots questions with detailed solutions 
 Tough and tricky PS exponents and roots questions with detailed solutions 
 Exponents DS Questions 
 Exponents PS Questions 
 Roots DS Questions 
 Roots PS Questions     
Check below for more:
 ALL YOU NEED FOR QUANT ! ! ! 
 Ultimate GMAT Quantitative Megathread

Hope it helps.

Root of (1620+832)=

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Root of (16*20+8*32)=

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Root of (1620+832)=