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Simplify \( \Large \sqrt[6]{ \left(27\right)^{-\frac{2}{3}} } + \left(8\right)^{-\frac{2}{3}} \)

A) \( \Large \sqrt[6]{35} \)
B) \( \Large \frac{6}{\sqrt{13}} \)
C) \( \Large \sqrt{13} \)
D) \( \Large \sqrt[6]{6} \)

Correct Answer:



C) \( \Large \sqrt{13} \)

Description for Correct answer:

\( \Large 6\sqrt{ \left(27\right)^{-\frac{2}{3}} + \left(8\right)^{-\frac{2}{3}} } = 6\sqrt{ \left(\frac{1}{27}\right)^{\frac{2}{3}} + \left(\frac{1}{8}\right)^{\frac{2}{3}} } \)

\( \Large 6\sqrt{ \left(\frac{1}{3^{3}}\right)^{\frac{2}{3}} } + \left(\frac{1}{2^{3}}\right)^{\frac{2}{3}} = 6\sqrt{\frac{1}{3^{2}} + \frac{1}{2^{2}}} \)

\( \Large 6\sqrt{\frac{1}{9} + \frac{1}{4}} = 6\sqrt{\frac{4+9}{36}} = 6 \times \frac{\sqrt{13}}{6} = \sqrt{13} \)

Part of solved Indices and Surd questions and answers : >> Elementary Mathematics >> Indices and Surd

Comments

Similar Questions

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