Basic Math Examples

$\sqrt{98 k^{7} q^{8}}$

Step 1

Rewrite $98 k^{7} q^{8}$ as ${(7 k^{3} q^{4})}^{2} \cdot (2 k)$ .

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Step 1.1

Factor $49$ out of $98$ .

$\sqrt{49 (2) k^{7} q^{8}}$

Step 1.2

Rewrite $49$ as $7^{2}$ .

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

Step 1.3

Factor out $k^{6}$ .

$\sqrt{7^{2} \cdot 2 (k^{6} k) q^{8}}$

Step 1.4

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

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

Step 1.5

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

$\sqrt{7^{2} \cdot 2 ({(k^{3})}^{2} k) {(q^{4})}^{2}}$

Step 1.6

Move $k$ .

$\sqrt{7^{2} \cdot 2 ({(k^{3})}^{2}) {(q^{4})}^{2} k}$

Step 1.7

Move $2$ .

$\sqrt{(7^{2} ({(k^{3})}^{2})) {(q^{4})}^{2} \cdot 2 k}$

Step 1.8

Rewrite $(7^{2} ({(k^{3})}^{2})) {(q^{4})}^{2}$ as ${(7 k^{3} q^{4})}^{2}$ .

$\sqrt{{(7 k^{3} q^{4})}^{2} \cdot 2 k}$

Step 1.9

Add parentheses.

$\sqrt{{(7 k^{3} q^{4})}^{2} \cdot (2 k)}$

Step 2

Pull terms out from under the radical.

$7 k^{3} q^{4} \sqrt{2 k}$