If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to

Question

If x = 4 and y = 16, then  \sqrt{\frac{x+y}{xy}}  is closet to which of the following?

A. 1/3
B. 1/2
C. 3/4
D. 7/8
E. 1

Bunuel · Accepted Answer

\sqrt{\frac{x+y}{xy}}=\sqrt{\frac{4+16}{4*16}}=\sqrt{\frac{20}{4*16}}=\sqrt{\frac{5}{16}}\approx{\sqrt{\frac{4}{16}}}=\sqrt{\frac{1}{4}}=\frac{1}{2} .

Answer: B.

P.S. Please format the questions correctly. Thank you.

BrentGMATPrepNow · Answer

Before test day, be sure to memorize the following approximations:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2

Useful property:  \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}

Given:  \sqrt{\frac{x+y}{xy}}

Substitute values:  \sqrt{\frac{4+16}{(4)(16)}}

Simplify:  \sqrt{\frac{20}{64}}

Apply above  property :  \frac{\sqrt{20}}{\sqrt{64}}

Rewrite numerator and simplify denominator:  \frac{2\sqrt{5}}{8}

Substitute 2.2 for √5 to get:  \frac{(2)(2.2)}{8} ≈ \frac{4.4}{8}

Since 1/2 closest answer choice to  \frac{4.4}{8} , the correct answer is B

sidoknowia · Answer

Hi  Bunuel ,

in your final step

\sqrt{\frac{5}{16}} = 2.73 / 4

2.73 is approx 3,
then answer becomes 3/4.

Why are we not solving it in this way?

Bunuel · Answer

\sqrt{5}\approx 2.24 , not 2.73

dave13 · Answer

Hi Bunuel , why my solution is not correct ? Any idea ?

\sqrt{\frac{4+16}{4*16}} = \frac{sqrt4 +sqrt16}{sqrt64} = \frac{3}{4}

Bunuel · Answer

Generally  \sqrt{x+y} 
eq \sqrt{x}+\sqrt{y} . Does  \sqrt{1+4}  equal to  \sqrt{1}+\sqrt{4} ?

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.

PrernaMurada · Answer

((x+y)/xy)^0.5
Substituting the value of x and y,Given expression=(20/4*16)^0.5
5^0.5/4=2.23/4 which is approximately 0.5

dave13 · Answer

Hello Bunuel , i have one question which i dont understnd What would equal 0^0 = 1? or = 0 ? many thanks

Bunuel · Answer

0^0, in some sources equals to 1, some mathematicians say it's undefined. But you won't need this for the GMAT because the case of 0^0 is not tested on the GMAT.

Abhishek009 · Answer

\sqrt{\frac{x+y}{xy}}

=  \sqrt{\frac{20}{64}}

=  \sqrt{\frac{10}{32}}

=  \sqrt{\frac{5}{16}}

~  \sqrt{\frac{4}{16}}

~  \sqrt{\frac{1}{4}}

~  \frac{1}{2} , Answer must be (B)

Hoozan · Answer

Bunuel  why isn't 2.24/4 not close to 3/4?

Bunuel · Answer

2.24/4 = 0.56 while 3/4 = 0.75.

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If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to

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If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to

Prep Toolkit

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