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Feb 03, 2025

If $\sqrt[4]{256} = n$ and $\sqrt[3]{- 27} = m$ , then m + n could equal which of the following?

I. 1

II. -1

III. 7

I only

I and II

I and III

III only

I, II, and III

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Scott Woodbury-Stewart Founder and Expert GMAT Instructor

Text Solution:

When solving this question, we may recall the following rule:

In general, if n is even, $\sqrt[n]{x^{n}} = |x|$ , and if n is odd, $\sqrt[n]{x^{n}} = x$ .

Thus, we know the following:

$\Rightarrow \sqrt[4]{256} = \sqrt[4]{4^{4}} = |4| = 4 = n$

$\Rightarrow \sqrt[3]{- 27} = \sqrt[3]{{(- 3)}^{3}} = - 3 = m$

There, the only value of m + n is 4 $-$ 3 = 1

Correct answer: A

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