Question

question
simplify \\(\sqrt4{16x^8}\\) completely given \\(x > 0\\).
answer attempt 1 out of 2

Explanation:

Step1: Rewrite radicand as 4th powers

$\sqrt[4]{16x^8} = \sqrt[4]{2^4 \cdot (x^2)^4}$

Step2: Apply 4th root property

$\sqrt[4]{2^4 \cdot (x^2)^4} = \sqrt[4]{2^4} \cdot \sqrt[4]{(x^2)^4}$

Step3: Evaluate each 4th root

Since $x>0$, $\sqrt[4]{2^4}=2$ and $\sqrt[4]{(x^2)^4}=x^2$

Step4: Multiply the results

$2 \cdot x^2 = 2x^2$

Answer:

$2x^2$