Basic Math Examples

$\frac{\sqrt{4 w y^{2}}}{\sqrt{6 w y^{3}}}$

Step 1

Combine $\sqrt{4 w y^{2}}$ and $\sqrt{6 w y^{3}}$ into a single radical.

$\sqrt{\frac{4 w y^{2}}{6 w y^{3}}}$

Step 2

Reduce the expression $\frac{4 w y^{2}}{6 w y^{3}}$ by cancelling the common factors.

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Step 2.1

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

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

Step 2.2

Factor $2$ out of $6 w y^{3}$ .

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

Step 2.3

Cancel the common factor.

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

Step 2.4

Rewrite the expression.

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

Step 3

Cancel the common factor of $w$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

Cancel the common factor of $y^{2}$ and $y^{3}$ .

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $y^{2}$ out of $3 y^{3}$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Rewrite $\sqrt{\frac{2}{3 y}}$ as $\frac{\sqrt{2}}{\sqrt{3 y}}$ .

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

Step 6

Multiply $\frac{\sqrt{2}}{\sqrt{3 y}}$ by $\frac{\sqrt{3 y}}{\sqrt{3 y}}$ .

$\frac{\sqrt{2}}{\sqrt{3 y}} \cdot \frac{\sqrt{3 y}}{\sqrt{3 y}}$

Step 7

Combine and simplify the denominator.

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Step 7.1

Multiply $\frac{\sqrt{2}}{\sqrt{3 y}}$ by $\frac{\sqrt{3 y}}{\sqrt{3 y}}$ .

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

Step 7.2

Raise $\sqrt{3 y}$ to the power of $1$ .

$\frac{\sqrt{2} \sqrt{3 y}}{{\sqrt{3 y}}^{1} \sqrt{3 y}}$

Step 7.3

Raise $\sqrt{3 y}$ to the power of $1$ .

$\frac{\sqrt{2} \sqrt{3 y}}{{\sqrt{3 y}}^{1} {\sqrt{3 y}}^{1}}$

Step 7.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt{2} \sqrt{3 y}}{{\sqrt{3 y}}^{1 + 1}}$

Step 7.5

Add $1$ and $1$ .

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

Step 7.6

Rewrite ${\sqrt{3 y}}^{2}$ as $3 y$ .

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Step 7.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 y}$ as ${(3 y)}^{\frac{1}{2}}$ .

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

Step 7.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 7.6.3

Combine $\frac{1}{2}$ and $2$ .

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

Step 7.6.4

Cancel the common factor of $2$ .

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Step 7.6.4.1

Cancel the common factor.

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

Step 7.6.4.2

Rewrite the expression.

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

Step 7.6.5

Simplify.

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

Step 8

Simplify the numerator.

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Step 8.1

Combine using the product rule for radicals.

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

Step 8.2

Multiply $2$ by $3$ .

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