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Lesson: 9.2 Simplifying Radicals
Question 8 of 10 , Step 1 of 1
$6 / 10$
Correct
Simplify the following expression. Assume that each variable is positive.
\[
\sqrt[3]{24 x^{5}}
\]

Answer

Answer

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Answer

Combine like terms: $2x^2 \sqrt[3]{3}$

Steps

Step 1 ：Factorize 24: $24 = 2^3 \times 3$

Step 2 ：Simplify $x^5$

Step 3 ：Rewrite the expression using prime factorization: $\sqrt[3]{24 x^{5}} = \sqrt[3]{2^3 \times 3 \times x \times x \times x \times x \times x}$

Step 4 ：Separate the factors under the cube root: $\sqrt[3]{2^3} \times \sqrt[3]{3} \times \sqrt[3]{x \times x \times x \times x \times x}$

Step 5 ：Simplify each cube root separately: $2 \times \sqrt[3]{3} \times x \times x$

Step 6 ：Combine like terms: $2x^2 \sqrt[3]{3}$