Simplify square root of 20b^3c^4

$\sqrt{20 b^{3} c^{4}}$

Step 1

Rewrite $20 b^{3} c^{4}$ as ${(2 b c^{2})}^{2} \cdot (5 b)$ .

Factor $4$ out of $20$ .

$\sqrt{4 (5) b^{3} c^{4}}$

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

$\sqrt{2^{2} \cdot 5 b^{3} c^{4}}$

Factor out $b^{2}$ .

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

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

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

Move $b$ .

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

Move $5$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$2 b c^{2} \sqrt{5 b}$