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555-605 (Medium)|   Arithmetic|   Roots|         
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eybrj2
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If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to Updated on: 07 Mar 2012, 00:56
Originally posted by eybrj2 on 06 Mar 2012, 23:29.
Last edited by Bunuel on 07 Mar 2012, 00:56, edited 1 time in total.
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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
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B
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If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to 07 Mar 2012, 00:53
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eybrj2
If x = 4 and y = 16, then \sqrt{x + y/xy} is closet to which of the following?

A. 1/3
B. 1/2
C. 3/4
D. 7/8
E 1
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\(\sqrt{\frac{x+y}{xy}}=\sqrt{\frac{4+16}{4*16}}=\sqrt{\frac{20}{4*16}}=\sqrt{\frac{5}{16}}\approx{\sqrt{\frac{4}{16}}}=\sqrt{\frac{1}{4}}=\frac{1}{2}\).

Answer: B.

P.S. Please format the questions correctly. Thank you.
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If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to 16 Oct 2016, 18:35
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Bunuel
eybrj2
If x = 4 and y = 16, then \sqrt{x + y/xy} is closet to which of the following?

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

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

Answer: B.

P.S. Please format the questions correctly. Thank you.
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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?
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If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to 17 Oct 2016, 03:05
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Bunuel
eybrj2
If x = 4 and y = 16, then \sqrt{x + y/xy} is closet to which of the following?

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

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

Answer: B.

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


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?
Show more

\(\sqrt{5}\approx 2.24\), not 2.73
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If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to 17 Feb 2018, 13:36
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eybrj2
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
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Hi Bunuel , why my solution is not correct ? Any idea ? :)

\(\sqrt{\frac{4+16}{4*16}}\) = \(\frac{sqrt4 +sqrt16}{sqrt64}\) = \(\frac{3}{4}\)
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If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to 17 Feb 2018, 15:17
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eybrj2
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

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

\(\sqrt{\frac{4+16}{4*16}}\) = \(\frac{sqrt4 +sqrt16}{sqrt64}\) = \(\frac{3}{4}\)
Show more

Generally \(\sqrt{x+y} \neq \sqrt{x}+\sqrt{y}\). Does \(\sqrt{1+4}\) equal to \(\sqrt{1}+\sqrt{4}\)?

8. Exponents and Roots of Numbers



Check below for more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.
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If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to 18 Feb 2018, 00:45
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((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
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If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to 18 Feb 2018, 03:43
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eybrj2
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

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

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

Generally \(\sqrt{x+y} \neq \sqrt{x}+\sqrt{y}\). Does \(\sqrt{1+4}\) equal to \(\sqrt{1}+\sqrt{4}\)?

8. Exponents and Roots of Numbers



Check below for more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.
Show more


Hello Bunuel, i have one question which i dont understnd

What would equal \(0^0\) = 1? or = 0 ?

many thanks :)
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If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to 18 Feb 2018, 05:25
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dave13

Hello Bunuel, i have one question which i dont understnd

What would equal \(0^0\) = 1? or = 0 ?

many thanks :)
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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.
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If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to 08 May 2020, 01:21
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eybrj2
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
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\(\sqrt{\frac{x+y}{xy}}\)

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

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

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

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

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

~ \(\frac{1}{2}\), Answer must be (B)
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If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to 23 Oct 2020, 03:53
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Quote:
\(\sqrt{5}\approx 2.24\), not 2.73
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Bunuel why isn't 2.24/4 not close to 3/4?
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If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to 23 Oct 2020, 07:09
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Quote:
\(\sqrt{5}\approx 2.24\), not 2.73

Bunuel why isn't 2.24/4 not close to 3/4?
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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 20 Apr 2022, 10:28
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eybrj2
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
Show more

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
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