Algebra Examples

$\frac{\sqrt{48 x^{3} y^{7}}}{\sqrt{8 x^{5} y}}$

Step 1

Combine $\sqrt{48 x^{3} y^{7}}$ and $\sqrt{8 x^{5} y}$ into a single radical.

$\sqrt{\frac{48 x^{3} y^{7}}{8 x^{5} y}}$

Step 2

Reduce the expression $\frac{48 x^{3} y^{7}}{8 x^{5} y}$ by cancelling the common factors.

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Step 2.1

Factor $8$ out of $48 x^{3} y^{7}$ .

$\sqrt{\frac{8 (6 x^{3} y^{7})}{8 x^{5} y}}$

Step 2.2

Factor $8$ out of $8 x^{5} y$ .

$\sqrt{\frac{8 (6 x^{3} y^{7})}{8 (x^{5} y)}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{8 (6 x^{3} y^{7})}{8 (x^{5} y)}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{6 x^{3} y^{7}}{x^{5} y}}$

Step 3

Cancel the common factor of $x^{3}$ and $x^{5}$ .

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Step 3.1

Factor $x^{3}$ out of $6 x^{3} y^{7}$ .

$\sqrt{\frac{x^{3} (6 y^{7})}{x^{5} y}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x^{3}$ out of $x^{5} y$ .

$\sqrt{\frac{x^{3} (6 y^{7})}{x^{3} (x^{2} y)}}$

Step 3.2.2

Cancel the common factor.

$\sqrt{\frac{x^{3} (6 y^{7})}{x^{3} (x^{2} y)}}$

Step 3.2.3

Rewrite the expression.

$\sqrt{\frac{6 y^{7}}{x^{2} y}}$

Step 4

Cancel the common factor of $y^{7}$ and $y$ .

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Step 4.1

Factor $y$ out of $6 y^{7}$ .

$\sqrt{\frac{y (6 y^{6})}{x^{2} y}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $y$ out of $x^{2} y$ .

$\sqrt{\frac{y (6 y^{6})}{y x^{2}}}$

Step 4.2.2

Cancel the common factor.

$\sqrt{\frac{y (6 y^{6})}{y x^{2}}}$

Step 4.2.3

Rewrite the expression.

$\sqrt{\frac{6 y^{6}}{x^{2}}}$

Step 5

Rewrite $\frac{6 y^{6}}{x^{2}}$ as ${(\frac{y^{3}}{x})}^{2} \cdot 6$ .

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Step 5.1

Factor the perfect power ${(y^{3})}^{2}$ out of $6 y^{6}$ .

$\sqrt{\frac{{(y^{3})}^{2} \cdot 6}{x^{2}}}$

Step 5.2

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

$\sqrt{\frac{{(y^{3})}^{2} \cdot 6}{x^{2} \cdot 1}}$

Step 5.3

Rearrange the fraction $\frac{{(y^{3})}^{2} \cdot 6}{x^{2} \cdot 1}$ .

$\sqrt{{(\frac{y^{3}}{x})}^{2} \cdot 6}$

Step 6

Pull terms out from under the radical.

$\frac{y^{3}}{x} \sqrt{6}$

Step 7

Combine $\frac{y^{3}}{x}$ and $\sqrt{6}$ .

$\frac{y^{3} \sqrt{6}}{x}$