Best solutions to - "Perform the indicated operation and express the answer..."

High School
Algebra
Algebra I
Exponents and radicals

Anish Buchanan

Answered question

2021-09-06

Perform the indicated operation and express the answer in simplest radical form.
$\sqrt[3]{9} \sqrt{3}$

Answer & Explanation

unett

Skilled2021-09-07Added 119 answers

To simplify $\sqrt[3]{9} \sqrt{3}$
Solution: $\sqrt[3]{9} \sqrt{3}$
On simplifying further we get:
$\Rightarrow \sqrt[3]{9} \sqrt{3} = {(9)}^{\frac{1}{3}} \cdot {(3)}^{\frac{1}{2}}$
$\Rightarrow \sqrt[3]{9} \sqrt{3} = {(3^{2})}^{\frac{1}{3}} \cdot {(3)}^{\frac{1}{2}}$
$\Rightarrow \sqrt[3]{9} \sqrt{3} = {(3)}^{\frac{2}{3}} \cdot {(3)}^{\frac{1}{2}}$
$\Rightarrow \sqrt[3]{9} \sqrt{3} = {(3)}^{\frac{2}{3} + \frac{1}{2}}$
$\Rightarrow \sqrt[3]{9} \sqrt{3} = {(3)}^{\frac{7}{6}}$
$\Rightarrow \sqrt[3]{9} \sqrt{3} = {(3^{7})}^{\frac{1}{6}}$
$\Rightarrow \sqrt[3]{9} \sqrt{3} = \sqrt{6} {3^{7}}$
Result:
$\sqrt[3]{9} \sqrt{3} = \sqrt[6]{3^{7}}$

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