Official Guide Explanation:
Problem Solving #11




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Solution and Metadata

Question: 11
Page: 153
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Powers and Roots of Numbers > Roots other than 2
Category 2: Arithmetic > Powers and Roots of Numbers > Roots

Explanation: When dealing with very small decimals, like 0.000064, it is often easier to rewrite them using scientific notation. 0.000064 = 64 * 10-6, so we can think of the question as rt[ 3rt[64 * 10-6]]. Start from the inside, and to make things simpler, think of 64 as 26. Thus, the first step is simplifying 3rt[26 * 10-6], which is equivalent to (26 * 10-6)1/3. Distributing the exponent, we get (26)1/3 * (10-6)1/3, or 22 * 10-2. The next step is keep working our way out of the radical signs: rt[22 * 10-2] = (22)1/2 * (10-2)1/2 = 2 * 10-1 = 0.2, which is choice (E).

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