Pre-Algebra Examples

$\frac{\sqrt{96 a^{5} b}}{\sqrt{3 a b^{3}}}$

Step 1

Combine $\sqrt{96 a^{5} b}$ and $\sqrt{3 a b^{3}}$ into a single radical.

$\sqrt{\frac{96 a^{5} b}{3 a b^{3}}}$

Step 2

Reduce the expression $\frac{96 a^{5} b}{3 a b^{3}}$ by cancelling the common factors.

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Step 2.1

Factor $3$ out of $96 a^{5} b$ .

$\sqrt{\frac{3 (32 a^{5} b)}{3 a b^{3}}}$

Step 2.2

Factor $3$ out of $3 a b^{3}$ .

$\sqrt{\frac{3 (32 a^{5} b)}{3 (a b^{3})}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{3 (32 a^{5} b)}{3 (a b^{3})}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{32 a^{5} b}{a b^{3}}}$

Step 3

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

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Step 3.1

Factor $a$ out of $32 a^{5} b$ .

$\sqrt{\frac{a (32 a^{4} b)}{a b^{3}}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $a$ out of $a b^{3}$ .

$\sqrt{\frac{a (32 a^{4} b)}{a (b^{3})}}$

Step 3.2.2

Cancel the common factor.

$\sqrt{\frac{a (32 a^{4} b)}{a b^{3}}}$

Step 3.2.3

Rewrite the expression.

$\sqrt{\frac{32 a^{4} b}{b^{3}}}$

Step 4

Cancel the common factor of $b$ and $b^{3}$ .

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Step 4.1

Factor $b$ out of $32 a^{4} b$ .

$\sqrt{\frac{b (32 a^{4})}{b^{3}}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $b$ out of $b^{3}$ .

$\sqrt{\frac{b (32 a^{4})}{b \cdot b^{2}}}$

Step 4.2.2

Cancel the common factor.

$\sqrt{\frac{b (32 a^{4})}{b \cdot b^{2}}}$

Step 4.2.3

Rewrite the expression.

$\sqrt{\frac{32 a^{4}}{b^{2}}}$

Step 5

Rewrite $\frac{32 a^{4}}{b^{2}}$ as ${(\frac{4 a^{2}}{b})}^{2} \cdot 2$ .

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Step 5.1

Factor the perfect power ${(4 a^{2})}^{2}$ out of $32 a^{4}$ .

$\sqrt{\frac{{(4 a^{2})}^{2} \cdot 2}{b^{2}}}$

Step 5.2

Factor the perfect power $b^{2}$ out of $b^{2}$ .

$\sqrt{\frac{{(4 a^{2})}^{2} \cdot 2}{b^{2} \cdot 1}}$

Step 5.3

Rearrange the fraction $\frac{{(4 a^{2})}^{2} \cdot 2}{b^{2} \cdot 1}$ .

$\sqrt{{(\frac{4 a^{2}}{b})}^{2} \cdot 2}$

Step 6

Pull terms out from under the radical.

$\frac{4 a^{2}}{b} \sqrt{2}$

Step 7

Combine $\frac{4 a^{2}}{b}$ and $\sqrt{2}$ .

$\frac{4 a^{2} \sqrt{2}}{b}$