Pre-Algebra Examples

$\frac{\sqrt{12 x y^{3}}}{\sqrt{6 x}}$

Step 1

Combine $\sqrt{12 x y^{3}}$ and $\sqrt{6 x}$ into a single radical.

$\sqrt{\frac{12 x y^{3}}{6 x}}$

Step 2

Reduce the expression $\frac{12 x y^{3}}{6 x}$ by cancelling the common factors.

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Step 2.1

Factor $6$ out of $12 x y^{3}$ .

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

Step 2.2

Factor $6$ out of $6 x$ .

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

Step 2.3

Cancel the common factor.

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

Step 2.4

Rewrite the expression.

$\sqrt{\frac{2 x y^{3}}{x}}$

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

$\sqrt{\frac{2 x y^{3}}{x}}$

Step 3.2

Divide $2 y^{3}$ by $1$ .

$\sqrt{2 y^{3}}$

Step 4

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

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Step 4.1

Factor out $y^{2}$ .

$\sqrt{2 (y^{2} y)}$

Step 4.2

Reorder $2$ and $y^{2}$ .

$\sqrt{y^{2} \cdot 2 y}$

Step 4.3

Add parentheses.

$\sqrt{y^{2} \cdot (2 y)}$

Step 5

Pull terms out from under the radical.

$y \sqrt{2 y}$