Question

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

Explanation:

Step1: Use property of square roots

We know that $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ (for $a\geq0,b\geq0$). So, $\sqrt{3x^{8}}=\sqrt{3}\cdot\sqrt{x^{8}}$.

Step2: Simplify $\sqrt{x^{8}}$

Using the property $\sqrt{x^{n}} = x^{\frac{n}{2}}$ (for $x\geq0$), when $n = 8$, we have $\sqrt{x^{8}}=x^{\frac{8}{2}}=x^{4}$.

Step3: Combine the results

Substitute $\sqrt{x^{8}} = x^{4}$ back into the expression from Step1, we get $\sqrt{3}\cdot x^{4}=x^{4}\sqrt{3}$.

Answer:

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