Question

express in simplest radical form assuming $x > 0$. $sqrt{3x^8}$ answer $\bigcirc sqrt{3x^8}$ $\bigcirc 3x^4$ $\bigcirc x^4sqrt{3x}$ $\bigcirc x^4sqrt{3}$

Explanation:

Step1: Use the property of square roots $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ (where $a = 3$ and $b = x^8$)

$\sqrt{3x^8}=\sqrt{3}\cdot\sqrt{x^8}$

Step2: Simplify $\sqrt{x^8}$ using the property $\sqrt{x^n}=x^{\frac{n}{2}}$ (for $x>0$ and $n$ even)

Since $n = 8$, $\sqrt{x^8}=x^{\frac{8}{2}}=x^4$

Step3: Combine the simplified terms

$\sqrt{3}\cdot\sqrt{x^8}=\sqrt{3}\cdot x^4=x^4\sqrt{3}$

Answer:

$x^4\sqrt{3}$ (corresponding to the option: $x^4\sqrt{3}$)