Expert Answer to "The simplified value of the radical expression 123"

Secondary
Algebra
Algebra II
Rational exponents and radicals

defazajx

Answered question

2021-07-30

The simplified value of the radical expression

\sqrt[3]{\frac{1}{2}}

Answer & Explanation

Ezra Herbert

Skilled2021-07-31Added 99 answers

Step 1
Formula:
$(\sqrt[n]{a})^{m} = \sqrt[n]{a^{m}}$
a) $\sqrt[n]{a b} = \sqrt[n]{a} \cdot \sqrt[n]{b}$
b) $\sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}}$
Step 2
a) $\sqrt[3]{\frac{1}{2}} = \sqrt[3]{\frac{1}{2}} \times \frac{\sqrt[3]{4}}{\sqrt[3]{4}}$
$= \sqrt[3]{\frac{4}{8}}$
$= \frac{\sqrt[3]{4}}{\sqrt[3]{8}}$
$= \frac{\sqrt[3]{4}}{\sqrt[3]{2^{3}}}$
b) $\sqrt[3]{\frac{1}{2}} = \frac{\sqrt[3]{4}}{(2^{3})^{1 / 3}}$
$= \frac{\sqrt[3]{4}}{2}$

Jeffrey Jordon

Expert2021-10-29Added 2575 answers

Answer is given below (on video)

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