Simplify square root of 175ab^9c^4

$\sqrt{175 a b^{9} c^{4}}$

Rewrite $175 a b^{9} c^{4}$ as ${(5 b^{4} c^{2})}^{2} \cdot (7 a b)$ .

Factor $25$ out of $175$ .

$\sqrt{25 (7) a b^{9} c^{4}}$

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

$\sqrt{5^{2} \cdot 7 a b^{9} c^{4}}$

Factor out $b^{8}$ .

$\sqrt{5^{2} \cdot 7 a (b^{8} b) c^{4}}$

Rewrite $b^{8}$ as ${(b^{4})}^{2}$ .

$\sqrt{5^{2} \cdot 7 a ({(b^{4})}^{2} b) c^{4}}$

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

$\sqrt{5^{2} \cdot 7 a ({(b^{4})}^{2} b) {(c^{2})}^{2}}$

Move $b$ .

$\sqrt{5^{2} \cdot 7 a ({(b^{4})}^{2}) {(c^{2})}^{2} b}$

Move $a$ .

$\sqrt{(5^{2} \cdot 7 ({(b^{4})}^{2})) {(c^{2})}^{2} a b}$

Move $7$ .

$\sqrt{(5^{2} ({(b^{4})}^{2})) {(c^{2})}^{2} \cdot 7 a b}$

Rewrite $(5^{2} ({(b^{4})}^{2})) {(c^{2})}^{2}$ as ${(5 b^{4} c^{2})}^{2}$ .

$\sqrt{{(5 b^{4} c^{2})}^{2} \cdot 7 a b}$

Add parentheses.

$\sqrt{{(5 b^{4} c^{2})}^{2} \cdot 7 (a b)}$

Add parentheses.

$\sqrt{{(5 b^{4} c^{2})}^{2} \cdot (7 a b)}$

Pull terms out from under the radical.

$5 b^{4} c^{2} \sqrt{7 a b}$