Simplify square root of 1575x^4

$\sqrt{1575 x^{4}}$

Step 1

Rewrite $1575 x^{4}$ as ${(15 x^{2})}^{2} \cdot 7$ .

Factor $225$ out of $1575$ .

$\sqrt{225 (7) x^{4}}$

Rewrite $225$ as $15^{2}$ .

$\sqrt{15^{2} \cdot 7 x^{4}}$

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

$\sqrt{15^{2} \cdot 7 {(x^{2})}^{2}}$

Move $7$ .

$\sqrt{15^{2} {(x^{2})}^{2} \cdot 7}$

Rewrite $15^{2} {(x^{2})}^{2}$ as ${(15 x^{2})}^{2}$ .

$\sqrt{{(15 x^{2})}^{2} \cdot 7}$

Step 2

Pull terms out from under the radical.

$15 x^{2} \sqrt{7}$