OG Square root of 16/81

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AbeNeedsAnswers: Master | Next Rank: 500 Posts; Posts: 394; Joined: Sun Jul 02, 2017 10:59 amFollowed by: 5 members; Thanked: 1 times

by AbeNeedsAnswers » Tue Jul 25, 2017 8:14 pm

If n = (16/81)^(1/2), what is the value of n^(1/2)?

(A) 1/9
(B) 1/4
(C) 4/9
(D) 2/3
(E) 9/2

D

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by Jay@ManhattanReview » Tue Jul 25, 2017 10:31 pm

AbeNeedsAnswers wrote:If n = (16/81)^(1/2), what is the value of n^(1/2)?

(A) 1/9
(B) 1/4
(C) 4/9
(D) 2/3
(E) 9/2

D

We have n = (16/81)^(1/2) = (4^2/9^2)^(1/2) = 4/9

n^(1/2) = (4/9)^(1/2)
n^(1/2) = (2^2/3^2)^(1/2) = [spoiler]2/3[/spoiler]

The correct answer: D

Hope this helps!

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Jabs80: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Tue Jul 25, 2017 11:46 pm

by Jabs80 » Tue Jul 25, 2017 11:48 pm

AbeNeedsAnswers wrote:If n = (16/81)^(1/2), what is the value of n^(1/2)?

(A) 1/9
(B) 1/4
(C) 4/9
(D) 2/3
(E) 9/2

D

4/9

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Jabs80: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Tue Jul 25, 2017 11:46 pm

by Jabs80 » Tue Jul 25, 2017 11:49 pm

Jabs80 wrote:
AbeNeedsAnswers wrote:If n = (16/81)^(1/2), what is the value of n^(1/2)?

(A) 1/9
(B) 1/4
(C) 4/9
(D) 2/3
(E) 9/2

D[/quote

2/3

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by DavidG@VeritasPrep » Wed Jul 26, 2017 4:11 am

Note also that when you take the root of a fraction between 0 and 1, the value of the fraction increases and moves closer to 1.
If n = 4/9, then âˆš (4/9) must be between 4/9 and 1. The only value in that range is 2/3. (Not that it's terribly difficult to find âˆš 4 and âˆš 9, but this property is helpful if you're given, say, âˆš .6.)

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by [email protected] » Wed Jul 26, 2017 6:58 pm

Jabs80 wrote:
AbeNeedsAnswers wrote:If n = (16/81)^(1/2), what is the value of n^(1/2)?

(A) 1/9
(B) 1/4
(C) 4/9
(D) 2/3
(E) 9/2

D
4/9

Hi Jabs80,

It looks like you caught your error, which is good. As you continue to study, you have to be mindful that the 4 wrong answers to any GMAT question are rarely 'random' - and some of those answers can be answers to DIFFERENT questions (so you have to be careful and make sure that you're answering the question that is ASKED). Here, while Answer C is the value of N, that is not what this question is asking for.

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

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon Aug 14, 2017 11:51 am

AbeNeedsAnswers wrote:If n = (16/81)^(1/2), what is the value of n^(1/2)?

(A) 1/9
(B) 1/4
(C) 4/9
(D) 2/3
(E) 9/2

D

We can simplify the given equation:

n = (16/81)^(1/2)

n = 4/9

Thus, n^(1/2) = 4/9^(1/2) = 2/3.

Answer: D

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Fri Aug 18, 2017 2:14 pm

The half power is the same as the square root, so for legibility's sake let's write:

n = âˆš16/81

n = 4/9

From here, âˆšn = âˆš4/9 = 2/3.

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Mon Feb 19, 2018 8:27 pm

Hi All,

When taking the square root of a fraction, you must take the square root of the numerator and the square root of the denominator.

Here, the square root of 16/81 = 4/9

We're then asked to calculate the square root of 4/9.... and that would be 2/3

Final Answer: D

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Rich

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