Simplify square root of 24x^7

$\sqrt{24 x^{7}}$

Step 1

Rewrite $24 x^{7}$ as ${(2 x^{3})}^{2} \cdot (6 x)$ .

Factor $4$ out of $24$ .

$\sqrt{4 (6) x^{7}}$

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

$\sqrt{2^{2} \cdot 6 x^{7}}$

Factor out $x^{6}$ .

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

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$\sqrt{2^{2} \cdot 6 ({(x^{3})}^{2} x)}$

Move $6$ .

$\sqrt{2^{2} {(x^{3})}^{2} \cdot 6 x}$

Rewrite $2^{2} {(x^{3})}^{2}$ as ${(2 x^{3})}^{2}$ .

$\sqrt{{(2 x^{3})}^{2} \cdot 6 x}$

Add parentheses.

$\sqrt{{(2 x^{3})}^{2} \cdot (6 x)}$

Step 2

Pull terms out from under the radical.

$2 x^{3} \sqrt{6 x}$