Question

express in simplest radical form assuming $x > 0$.
$sqrt{16x^5}$
answer
$\circ$ $x^2\sqrt{16x}$ $\circ$ $4x^2\sqrt{x}$
$\circ$ $\sqrt{16x^5}$ $\circ$ $4\sqrt{x^5}$

Explanation:

Step1: Split radical into factors

$\sqrt{16x^5} = \sqrt{16} \cdot \sqrt{x^5}$

Step2: Simplify $\sqrt{16}$

$\sqrt{16} = 4$

Step3: Rewrite $x^5$ for simplification

$\sqrt{x^5} = \sqrt{x^4 \cdot x} = \sqrt{x^4} \cdot \sqrt{x}$

Step4: Simplify $\sqrt{x^4}$

$\sqrt{x^4} = x^2$ (since $x>0$)

Step5: Combine simplified terms

$4 \cdot x^2 \cdot \sqrt{x} = 4x^2\sqrt{x}$

Answer:

B. $4x^2\sqrt{x}$