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: