Algebra Examples

$\sqrt{\frac{54 x^{6} y^{2}}{6 y^{4}}}$

Step 1

Reduce the expression $\frac{54 x^{6} y^{2}}{6 y^{4}}$ by cancelling the common factors.

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Step 1.1

Factor $6$ out of $54 x^{6} y^{2}$ .

$\sqrt{\frac{6 (9 x^{6} y^{2})}{6 y^{4}}}$

Step 1.2

Factor $6$ out of $6 y^{4}$ .

$\sqrt{\frac{6 (9 x^{6} y^{2})}{6 (y^{4})}}$

Step 1.3

Cancel the common factor.

$\sqrt{\frac{6 (9 x^{6} y^{2})}{6 y^{4}}}$

Step 1.4

Rewrite the expression.

$\sqrt{\frac{9 x^{6} y^{2}}{y^{4}}}$

Step 2

Cancel the common factor of $y^{2}$ and $y^{4}$ .

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Step 2.1

Factor $y^{2}$ out of $9 x^{6} y^{2}$ .

$\sqrt{\frac{y^{2} (9 x^{6})}{y^{4}}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $y^{2}$ out of $y^{4}$ .

$\sqrt{\frac{y^{2} (9 x^{6})}{y^{2} y^{2}}}$

Step 2.2.2

Cancel the common factor.

$\sqrt{\frac{y^{2} (9 x^{6})}{y^{2} y^{2}}}$

Step 2.2.3

Rewrite the expression.

$\sqrt{\frac{9 x^{6}}{y^{2}}}$

Step 3

Rewrite $9 x^{6}$ as ${(3 x^{3})}^{2}$ .

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

Step 4

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

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

Step 5

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

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