## How do you simplify \(\sqrt{x^{4}} ?\)

Answer:

See a solution process below:

Explanation:

We can rewrite the radical as:

\(\sqrt{x^{4}} \Rightarrow \sqrt{x^{2} \cdot x^{2}}\)

The square root is the the term multiplied by itself which equals the term within the radical. Therefore:

\(\sqrt{x^{2} \cdot x^{2}}=x^{2}\)We can also solve this using rules for exponents and radicals.

First we can rewrite the expression using this rule:

\(\sqrt[n]{x}=x^{\frac{1}{n}}\) \(\sqrt{x^{4}} \Rightarrow \sqrt[2]{x^{4}}=\left(x^{4}\right)^{\frac{1}{2}}\)Next, we can use this rule of exponents to simplify this result:

\(\left(x^{a}\right)^{b}=x^{a \times b}\) \(\left(x^{4}\right)^{\frac{1}{2}} \Rightarrow x^{4 \times \frac{1}{2}} \Rightarrow x^{\frac{4}{2}} \Rightarrow x^{2}\)