Simplify square root of 75x^12

$\sqrt{75 x^{12}}$

Step 1

Rewrite $75 x^{12}$ as ${(5 x^{6})}^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$\sqrt{25 (3) x^{12}}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 3 x^{12}}$

Rewrite $x^{12}$ as ${(x^{6})}^{2}$ .

$\sqrt{5^{2} \cdot 3 {(x^{6})}^{2}}$

Move $3$ .

$\sqrt{5^{2} {(x^{6})}^{2} \cdot 3}$

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

$\sqrt{{(5 x^{6})}^{2} \cdot 3}$

Step 2

Pull terms out from under the radical.

$5 x^{6} \sqrt{3}$