To simplify the expression \sqrt[3]{\frac{7}{8x^{3}}}

Question

To simplify the expression \sqrt[3]{\frac{7}{8x^{3}}}

Serotoninl7 2021-11-07 Answered

To simplify the expression $\sqrt[3]{\frac{7}{8 x^{3}}}$

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Expert Answer

Louise Eldridge

Answered 2021-11-08 Author has 17 answers

Calculation:
According to quotient property of square root $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$
And the product property of square root states $\sqrt{a b} = \sqrt{a} \cdot \sqrt{b}$ .
Given expression is $\sqrt[3]{\frac{7}{8 x^{3}}}$
This can be written as $\sqrt[3]{\frac{7}{8 x^{3}}} = \sqrt[3]{\frac{7}{2 \times 2 \times 2 \times x^{3}}}$
$\sqrt[3]{\frac{7}{8 x^{3}}} = \sqrt[3]{\frac{7}{2 \times 2 \times 2 \times x^{3}}}$
Applying the quotient rule,
$\sqrt[3]{\frac{7}{8 x^{3}}} = \frac{\sqrt[3]{7}}{\sqrt[3]{2 \times 2 \times 2 \times x^{3}}}$
Applying the product rule for Denominator,
$\sqrt[3]{\frac{7}{8 x^{3}}} = \frac{\sqrt[3]{7}}{\sqrt[3]{(2)^{3} \times \sqrt[3]{x^{3}}}}$
$\sqrt[3]{\frac{7}{8 x^{3}}} = \frac{\sqrt[3]{7}}{2 x}$

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