Processing math: 100%

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Simplify square root of (v^11)/49

$\sqrt{\frac{v^{11}}{49}}$

Step 1

Rewrite

$\frac{v^{11}}{49}$ as

${(\frac{v^{5}}{7})}^{2} v$ .

Factor the perfect power

${(v^{5})}^{2}$ out of

$v^{11}$ .

$\sqrt{\frac{{(v^{5})}^{2} v}{49}}$

Factor the perfect power

$7^{2}$ out of

$49$ .

$\sqrt{\frac{{(v^{5})}^{2} v}{7^{2} \cdot 1}}$

Rearrange the fraction

$\frac{{(v^{5})}^{2} v}{7^{2} \cdot 1}$ .

$\sqrt{{(\frac{v^{5}}{7})}^{2} v}$

$\sqrt{{(\frac{v^{5}}{7})}^{2} v}$

Step 2

Pull terms out from under the radical.

$\frac{v^{5}}{7} \sqrt{v}$

Step 3

Combine

$\frac{v^{5}}{7}$ and

$\sqrt{v}$ .

$\frac{v^{5} \sqrt{v}}{7}$

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