Basic Math Examples

$\sqrt{54 v^{21}}$

Step 1

Rewrite $54 v^{21}$ as ${(3 v^{10})}^{2} \cdot (6 v)$ .

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Step 1.1

Factor $9$ out of $54$ .

$\sqrt{9 (6) v^{21}}$

Step 1.2

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

$\sqrt{3^{2} \cdot 6 v^{21}}$

Step 1.3

Factor out $v^{20}$ .

$\sqrt{3^{2} \cdot 6 (v^{20} v)}$

Step 1.4

Rewrite $v^{20}$ as ${(v^{10})}^{2}$ .

$\sqrt{3^{2} \cdot 6 ({(v^{10})}^{2} v)}$

Step 1.5

Move $6$ .

$\sqrt{3^{2} {(v^{10})}^{2} \cdot 6 v}$

Step 1.6

Rewrite $3^{2} {(v^{10})}^{2}$ as ${(3 v^{10})}^{2}$ .

$\sqrt{{(3 v^{10})}^{2} \cdot 6 v}$

Step 1.7

Add parentheses.

$\sqrt{{(3 v^{10})}^{2} \cdot (6 v)}$

Step 2

Pull terms out from under the radical.

$3 v^{10} \sqrt{6 v}$