Simplify square root of 75k^7q^8

$\sqrt{75 k^{7} q^{8}}$

Step 1

Rewrite $75 k^{7} q^{8}$ as ${(5 k^{3} q^{4})}^{2} \cdot (3 k)$ .

Factor $25$ out of $75$ .

$\sqrt{25 (3) k^{7} q^{8}}$

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

$\sqrt{5^{2} \cdot 3 k^{7} q^{8}}$

Factor out $k^{6}$ .

$\sqrt{5^{2} \cdot 3 (k^{6} k) q^{8}}$

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

$\sqrt{5^{2} \cdot 3 ({(k^{3})}^{2} k) q^{8}}$

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

$\sqrt{5^{2} \cdot 3 ({(k^{3})}^{2} k) {(q^{4})}^{2}}$

Move $k$ .

$\sqrt{5^{2} \cdot 3 ({(k^{3})}^{2}) {(q^{4})}^{2} k}$

Move $3$ .

$\sqrt{(5^{2} ({(k^{3})}^{2})) {(q^{4})}^{2} \cdot 3 k}$

Rewrite $(5^{2} ({(k^{3})}^{2})) {(q^{4})}^{2}$ as ${(5 k^{3} q^{4})}^{2}$ .

$\sqrt{{(5 k^{3} q^{4})}^{2} \cdot 3 k}$

Add parentheses.

$\sqrt{{(5 k^{3} q^{4})}^{2} \cdot (3 k)}$

Step 2

Pull terms out from under the radical.

$5 k^{3} q^{4} \sqrt{3 k}$