Q. 117 - Intermediate Algebra

Question

Explain how you know that

$\sqrt[5]{x^{10}}=x^2$

Step-by-Step Solution

Answer

Thus, $\sqrt[5]{x^{10}}=x^2$. Hence proved.

Step 1. Given information.

Given expression,

$\sqrt[5]{x^{10}}$.

Step 2. Write the concept.

For a given expression, there will exist largest factor in the radical that is a perfect power of index. Now, use the product rule and rewrite the radical as product of two radical.

Also, simplify the root of perfect power.

Step 3. Calculation.

Given expression $\sqrt[5]{x^{10}}=x^2$

$$\begin{gathered} \sqrt[5]{x^{10}}=\sqrt[5]{{\left(x^2\right)}^5} \\ =x^2 \end{gathered}$$