Precalculus Examples

$\sqrt{\frac{16 u^{3} v}{u v^{5}}}$

Step 1

Reduce the expression $\frac{16 u^{3} v}{u v^{5}}$ by cancelling the common factors.

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Step 1.1

Factor $u$ out of $16 u^{3} v$ .

$\sqrt{\frac{u (16 u^{2} v)}{u v^{5}}}$

Step 1.2

Factor $u$ out of $u v^{5}$ .

$\sqrt{\frac{u (16 u^{2} v)}{u (v^{5})}}$

Step 1.3

Cancel the common factor.

$\sqrt{\frac{u (16 u^{2} v)}{u v^{5}}}$

Step 1.4

Rewrite the expression.

$\sqrt{\frac{16 u^{2} v}{v^{5}}}$

Step 2

Cancel the common factor of $v$ and $v^{5}$ .

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Step 2.1

Factor $v$ out of $16 u^{2} v$ .

$\sqrt{\frac{v (16 u^{2})}{v^{5}}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $v$ out of $v^{5}$ .

$\sqrt{\frac{v (16 u^{2})}{v \cdot v^{4}}}$

Step 2.2.2

Cancel the common factor.

$\sqrt{\frac{v (16 u^{2})}{v \cdot v^{4}}}$

Step 2.2.3

Rewrite the expression.

$\sqrt{\frac{16 u^{2}}{v^{4}}}$

Step 3

Rewrite $16 u^{2}$ as ${(4 u)}^{2}$ .

$\sqrt{\frac{{(4 u)}^{2}}{v^{4}}}$

Step 4

Rewrite $v^{4}$ as ${(v^{2})}^{2}$ .

$\sqrt{\frac{{(4 u)}^{2}}{{(v^{2})}^{2}}}$

Step 5

Rewrite $\frac{{(4 u)}^{2}}{{(v^{2})}^{2}}$ as ${(\frac{4 u}{v^{2}})}^{2}$ .

$\sqrt{{(\frac{4 u}{v^{2}})}^{2}}$

Step 6

Pull terms out from under the radical, assuming positive real numbers.

$\frac{4 u}{v^{2}}$