Simplify square root of 25x^7

$\sqrt{25 x^{7}}$

Rewrite $25 x^{7}$ as ${(5 x^{3})}^{2} x$ .

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

$\sqrt{5^{2} x^{7}}$

Factor out $x^{6}$ .

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

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

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

Rewrite $5^{2} {(x^{3})}^{2}$ as ${(5 x^{3})}^{2}$ .

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

Pull terms out from under the radical.

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