Basic Math Examples

$\sqrt{27 v^{14}}$

Step 1

Rewrite $27 v^{14}$ as ${(3 v^{7})}^{2} \cdot 3$ .

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Step 1.1

Factor $9$ out of $27$ .

$\sqrt{9 (3) v^{14}}$

Step 1.2

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 3 v^{14}}$

Step 1.3

Rewrite $v^{14}$ as ${(v^{7})}^{2}$ .

$\sqrt{3^{2} \cdot 3 {(v^{7})}^{2}}$

Step 1.4

Move $3$ .

$\sqrt{3^{2} {(v^{7})}^{2} \cdot 3}$

Step 1.5

Rewrite $3^{2} {(v^{7})}^{2}$ as ${(3 v^{7})}^{2}$ .

$\sqrt{{(3 v^{7})}^{2} \cdot 3}$

Step 2

Pull terms out from under the radical.

$3 v^{7} \sqrt{3}$