Official Guide Explanation:
Problem Solving #32

Background

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Solution and Metadata

Question: 32
Page: 156
Difficulty: 4 (Moderately Easy)
Category 1: Arithmetic > Powers and Roots of Numbers > Roots

Explanation: This is a classic example of the GMAT offering a problem that has a "right way" and a "better way." The "right way" involves multiplying 16 by 20 and 8 by 32, then finding the square root of 576. It works, but it's slow and prone to error. Instead, look for numbers that can be quickly and easily factored out of both terms, as follows:

rt[(16)(20) + (8)(32)]

= rt[(16)(20 + (8)(2))]

= 4 rt[(20 + 16)]

= 4 rt[36]

= 4(6) = 24, choice (B).

There are a variety of different ways to work through this problem, but the most efficient of them resemble the steps shown here.

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