Simplify square root of 24x^5

$\sqrt{24 x^{5}}$

Step 1

Rewrite $24 x^{5}$ as ${(2 x^{2})}^{2} \cdot (6 x)$ .

Factor $4$ out of $24$ .

$\sqrt{4 (6) x^{5}}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 6 x^{5}}$

Factor out $x^{4}$ .

$\sqrt{2^{2} \cdot 6 (x^{4} x)}$

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$\sqrt{2^{2} \cdot 6 ({(x^{2})}^{2} x)}$

Move $6$ .

$\sqrt{2^{2} {(x^{2})}^{2} \cdot 6 x}$

Rewrite $2^{2} {(x^{2})}^{2}$ as ${(2 x^{2})}^{2}$ .

$\sqrt{{(2 x^{2})}^{2} \cdot 6 x}$

Add parentheses.

$\sqrt{{(2 x^{2})}^{2} \cdot (6 x)}$

Step 2

Pull terms out from under the radical.

$2 x^{2} \sqrt{6 x}$