Chapter A.1, Problem 35E

Solution

Simplify by removing factors from the radicand.

  $2x^2\sqrt[5]{3}$ .

Given:

The given expression is $\sqrt[5]{96x^{10}}$ .

Concept Used:

• Find the largest factor in the radicand that is a perfect power of the index. Rewrite the radicand as a product of two factors, using that factor.
• Use the product rule to rewrite the radical as the product of two radicals.
• Simplify the root of the perfect power.

Calculation:

The given expression is $\sqrt[5]{96x^{10}}$ .

Let $a=\sqrt[5]{96x^{10}}$

  $\begin{array}{l}$ a={(96x^{10})}^{1/5}$a={\left(2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 3\cdot x^5\cdot x^5\right)}^{1/5}\\ a={\left(2^5\cdot 3\cdot x^5\cdot x^5\right)}^{1/5}\\ a=2\cdot x\cdot x{\left(3\right)}^{1/5}\\ a=2x^2\sqrt[5]{3}\end{array}$

Thus the solution of given expression $\sqrt[5]{96x^{10}}$ is $2x^2\sqrt[5]{3}$ .