Algebra Examples

$\frac{\sqrt{12 x^{4} y^{6}}}{\sqrt{x^{4}}}$

Step 1

Combine $\sqrt{12 x^{4} y^{6}}$ and $\sqrt{x^{4}}$ into a single radical.

$\sqrt{\frac{12 x^{4} y^{6}}{x^{4}}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Reduce the expression $\frac{12 x^{4} y^{6}}{x^{4}}$ by cancelling the common factors.

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Step 2.1.1

Cancel the common factor.

$\sqrt{\frac{12 x^{4} y^{6}}{x^{4}}}$

Step 2.1.2

Rewrite the expression.

$\sqrt{\frac{12 y^{6}}{1}}$

Step 2.2

Divide $12 y^{6}$ by $1$ .

$\sqrt{12 y^{6}}$

Step 3

Rewrite $12 y^{6}$ as ${(2 y^{3})}^{2} \cdot 3$ .

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Step 3.1

Factor $4$ out of $12$ .

$\sqrt{4 (3) y^{6}}$

Step 3.2

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 3 y^{6}}$

Step 3.3

Rewrite $y^{6}$ as ${(y^{3})}^{2}$ .

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

Step 3.4

Move $3$ .

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

Step 3.5

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

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

Step 4

Pull terms out from under the radical.

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