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## Nice fast way??

tagged by: Brent@GMATPrepNow

This topic has 4 expert replies and 0 member replies
boomgoesthegmat Senior | Next Rank: 100 Posts
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#### Nice fast way??

Mon Apr 25, 2016 2:37 pm
Which of the following is the value of squareroot[cuberoot(0.000064)]?

A) 0.004
B) 0.008
C) 0.02
D) 0.04
E) 0.2

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GMATGuruNY GMAT Instructor
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Mon Apr 25, 2016 2:58 pm
boomgoesthegmat wrote:
Which of the following is the value of squareroot[cuberoot(0.000064)]?

A) 0.004
B) 0.008
C) 0.02
D) 0.04
E) 0.2
[ (0.000064)^(1/3) ]^1/2

= (64 * 10¯⁶)^(1/6)

= (64)^(1/6) * (10¯⁶)^(1/6)

= 2 * 10¯¹

= 0.2

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Brent@GMATPrepNow GMAT Instructor
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Mon Apr 25, 2016 3:36 pm
boomgoesthegmat wrote:
Which of the following is the value of squareroot[cuberoot(0.000064)]?

A) 0.004
B) 0.008
C) 0.02
D) 0.04
E) 0.2
Another approach:

√[∛(0.000064)] = √[∛(64/1,000,000)]
= √[(4/100)]
= 2/10
= 0.2
= C

Here are some related resources that cover the concepts needed to solve this question:
- Conversions with fractions and decimals: https://www.gmatprepnow.com/module/gmat-arithmetic/video/1066
- Introduction to square roots: https://www.gmatprepnow.com/module/gmat-powers-and-roots/video/1033
- Other roots: https://www.gmatprepnow.com/module/gmat-powers-and-roots/video/1035

Cheers,
Brent

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Matt@VeritasPrep GMAT Instructor
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Wed Apr 27, 2016 2:12 pm
I'd think of it as

.000064^(1/2 * 1/3) =>

.000064^(1/6)

Since 2⁶ = 64, this suggests that the answer is .02 or .2. Then we might notice that .000064 has SIX decimal places. .2⁶ will also have six decimal places, so that MUST be our answer!

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Scott@TargetTestPrep GMAT Instructor
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Thu Mar 15, 2018 9:26 am
boomgoesthegmat wrote:
Which of the following is the value of squareroot[cuberoot(0.000064)]?

A) 0.004
B) 0.008
C) 0.02
D) 0.04
E) 0.2
To solve this question, we can refer to two rules:

1) If a decimal with a finite number of decimal places is a perfect cube, its cube root will have exactly one-third of the number of decimal places. Thus, a perfect cube decimal must have a number of decimal places that is a multiple of 3.

2) If a decimal with a finite number of decimal places is a perfect square, its square root will have exactly half of the number of decimal places. Thus, a perfect square decimal must have an even number of decimal places.

Let's look first at cuberoot(0.000064). By rule number 1, the cube root of 0.000064 = 0.04. We were able obtain this value because 0.000064 has 6 DECIMAL PLACES, and because the cube root of 64 is 4.

The problem now looks like this: squareroot(0.04). By rule number 2, the square root of 0.04 = 0.2. We were able to obtain this value because 0.04 has 2 DECIMAL PLACES, and the square root of 4 is 2.

Alternate Solution:

First, we note that taking the cube root of the square root of a number is equivalent to taking the sixth root of the number.

Next, let’s write 0.000064 = 64/1000000 = 2^6/10^6. Taking sixth root, we obtain 2/10 = 0.2.

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