Basic Math Examples

$\frac{4 \sqrt{225 y^{3}}}{7 \sqrt{3 y^{- 1}}}$

Step 1

Combine $\sqrt{225 y^{3}}$ and $\sqrt{3 y^{- 1}}$ into a single radical.

$\frac{4 \sqrt{\frac{225 y^{3}}{3 y^{- 1}}}}{7}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $225$ and $3$ .

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Step 2.1.1

Factor $3$ out of $225 y^{3}$ .

$\frac{4 \sqrt{\frac{3 (75 y^{3})}{3 y^{- 1}}}}{7}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $3$ out of $3 y^{- 1}$ .

$\frac{4 \sqrt{\frac{3 (75 y^{3})}{3 (y^{- 1})}}}{7}$

Step 2.1.2.2

Cancel the common factor.

$\frac{4 \sqrt{\frac{3 (75 y^{3})}{3 y^{- 1}}}}{7}$

Step 2.1.2.3

Rewrite the expression.

$\frac{4 \sqrt{\frac{75 y^{3}}{y^{- 1}}}}{7}$

Step 2.2

Cancel the common factor of $y^{3}$ and $y^{- 1}$ .

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Step 2.2.1

Factor $y^{- 1}$ out of $75 y^{3}$ .

$\frac{4 \sqrt{\frac{y^{- 1} (75 y^{4})}{y^{- 1}}}}{7}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Multiply by $1$ .

$\frac{4 \sqrt{\frac{y^{- 1} (75 y^{4})}{y^{- 1} \cdot 1}}}{7}$

Step 2.2.2.2

Cancel the common factor.

$\frac{4 \sqrt{\frac{y^{- 1} (75 y^{4})}{y^{- 1} \cdot 1}}}{7}$

Step 2.2.2.3

Rewrite the expression.

$\frac{4 \sqrt{\frac{75 y^{4}}{1}}}{7}$

Step 2.2.2.4

Divide $75 y^{4}$ by $1$ .

$\frac{4 \sqrt{75 y^{4}}}{7}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $75 y^{4}$ as ${(5 y^{2})}^{2} \cdot 3$ .

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Step 3.1.1

Factor $25$ out of $75$ .

$\frac{4 \sqrt{25 (3) y^{4}}}{7}$

Step 3.1.2

Rewrite $25$ as $5^{2}$ .

$\frac{4 \sqrt{5^{2} \cdot 3 y^{4}}}{7}$

Step 3.1.3

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

$\frac{4 \sqrt{5^{2} \cdot 3 {(y^{2})}^{2}}}{7}$

Step 3.1.4

Move $3$ .

$\frac{4 \sqrt{5^{2} {(y^{2})}^{2} \cdot 3}}{7}$

Step 3.1.5

Rewrite $5^{2} {(y^{2})}^{2}$ as ${(5 y^{2})}^{2}$ .

$\frac{4 \sqrt{{(5 y^{2})}^{2} \cdot 3}}{7}$

Step 3.2

Pull terms out from under the radical.

$\frac{4 \cdot 5 y^{2} \sqrt{3}}{7}$

Step 3.3

Multiply $4$ by $5$ .

$\frac{20 y^{2} \sqrt{3}}{7}$