Official Guide Explanation:
Problem Solving #117

Background

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Solution and Metadata

Question: 117
Page: 168
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Simplifying Algebraic Expressions >
Category 2: Arithmetic > Powers and Roots of Numbers > Roots

Explanation: As a general rule, when you need to simplify an expression with radicals in the denominator, use the principle of difference of squares. In this case, since the denominator is rt[n + 1]- rt[n], multiply the top and bottom of the fraction by rt[n + 1]+ rt[n]. Then simplify:

(1/( rt[n + 1]- rt[n])) * (( rt[n + 1]+ rt[n])/( rt[n + 1]+ rt[n]))

= (( rt[n + 1]+ rt[n])/(( rt[n + 1]- rt[n])( rt[n + 1]+ rt[n])))

= (( rt[n + 1]+ rt[n])/((n + 1) - n))

= (( rt[n + 1]+ rt[n])/1)= rt[n + 1]+ rt[n], choice (E).

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