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Re: What is the cube root of w? [#permalink]
06 Aug 2012, 02:15

3

This post received KUDOS

Expert's post

SOLUTION

What is the cube root of w?

(1) The 5th root of w is 64 --> \(\sqrt[5]{w}=64\) --> we can find \(w\), hence we can find \(\sqrt[3]{w}\): \(w=64^5\) --> \(\sqrt[3]{w}=\sqrt[3]{64^5}\). Sufficient.

(2) The 15th root of w is 4 --> \(\sqrt[15]{w}=4\). The same here. Sufficient.

Re: What is the cube root of w? [#permalink]
06 Aug 2012, 02:31

4

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1. If the nth root is asked for a number X: If n is odd - It has a unique solution that satisfies. On the other hand, if n is even - then both (y)^n and (-y)^n satisfies the solution. Now to the problem: A - sufficient. 5th root - 5 odd. B - sufficient. - 15 -odd.

Re: What is the cube root of w? [#permalink]
06 Aug 2012, 06:52

1

This post received KUDOS

This is a simple Surd problem i will rate its difficulty at 500 or below. as the first step break all numbers down to their basic form 64 = 4^3 = 2^6 ( we will find later that the second part is not necessary in this question, but in some other question we might need to break down further) Lets take statement 1 : (w)^1/3 = 64 this means w = 64^3 = 4^15 = 2^30 ( stop ! much before this coz you knwo you can find it ) Second statement (w)^1/15 = 4 This means w = 4^15 = 2^30 ( Stop as soon as you know it is solvable) So choice D is the nswer.

Re: What is the cube root of w? [#permalink]
10 Aug 2012, 04:10

Expert's post

SOLUTION

What is the cube root of w?

(1) The 5th root of w is 64 --> \(\sqrt[5]{w}=64\) --> we can find \(w\), hence we can find \(\sqrt[3]{w}\): \(w=64^5\) --> \(\sqrt[3]{w}=\sqrt[3]{64^5}\). Sufficient.

(2) The 15th root of w is 4 --> \(\sqrt[15]{w}=4\). The same here. Sufficient.

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