Precalculus (6th Edition)

Published by Pearson

Chapter R - Review of Basic Concepts - R.7 Radical Expressions - R.7 Exercises - Page 74: 34

Answer

Option ($D$). Simplified form: $\dfrac{\sqrt3}{2}$

Work Step by Step

A radical expression is not yet simplified when: (1) there is a radical in the denominator; or (2) the radicand still has a factor that is a perfect root of the index. Note that the radical expression in Option (D) has a denominator inside the radical sign. Thus, it is not yet in simplified form. To simplify the expression in $D$, factor each radicand so that one factor is a perfect square to obtain: $=\sqrt{\dfrac{3}{2^2}}$ Using the rule $\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}. a\gt0, b\gt0$, the expression above simplifies to: $=\dfrac{\sqrt{3}}{\sqrt{2^2}} \\=\color{blue}{\dfrac{\sqrt{3}}{2}}$

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