Finite Math Examples

$\frac{\sqrt{25 x}}{\sqrt{5 y}}$

Step 1

Combine $\sqrt{25 x}$ and $\sqrt{5 y}$ into a single radical.

$\sqrt{\frac{25 x}{5 y}}$

Step 2

Reduce the expression $\frac{25 x}{5 y}$ by cancelling the common factors.

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Step 2.1

Factor $5$ out of $25 x$ .

$\sqrt{\frac{5 (5 x)}{5 y}}$

Step 2.2

Factor $5$ out of $5 y$ .

$\sqrt{\frac{5 (5 x)}{5 (y)}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{5 (5 x)}{5 y}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{5 x}{y}}$

Step 3

Rewrite $\sqrt{\frac{5 x}{y}}$ as $\frac{\sqrt{5 x}}{\sqrt{y}}$ .

$\frac{\sqrt{5 x}}{\sqrt{y}}$

Step 4

Multiply $\frac{\sqrt{5 x}}{\sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

$\frac{\sqrt{5 x}}{\sqrt{y}} \cdot \frac{\sqrt{y}}{\sqrt{y}}$

Step 5

Combine and simplify the denominator.

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Step 5.1

Multiply $\frac{\sqrt{5 x}}{\sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

$\frac{\sqrt{5 x} \sqrt{y}}{\sqrt{y} \sqrt{y}}$

Step 5.2

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

$\frac{\sqrt{5 x} \sqrt{y}}{{\sqrt{y}}^{1} \sqrt{y}}$

Step 5.3

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

$\frac{\sqrt{5 x} \sqrt{y}}{{\sqrt{y}}^{1} {\sqrt{y}}^{1}}$

Step 5.4

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

$\frac{\sqrt{5 x} \sqrt{y}}{{\sqrt{y}}^{1 + 1}}$

Step 5.5

Add $1$ and $1$ .

$\frac{\sqrt{5 x} \sqrt{y}}{{\sqrt{y}}^{2}}$

Step 5.6

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

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Step 5.6.1

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

$\frac{\sqrt{5 x} \sqrt{y}}{{(y^{\frac{1}{2}})}^{2}}$

Step 5.6.2

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

$\frac{\sqrt{5 x} \sqrt{y}}{y^{\frac{1}{2} \cdot 2}}$

Step 5.6.3

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

$\frac{\sqrt{5 x} \sqrt{y}}{y^{\frac{2}{2}}}$

Step 5.6.4

Cancel the common factor of $2$ .

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Step 5.6.4.1

Cancel the common factor.

$\frac{\sqrt{5 x} \sqrt{y}}{y^{\frac{2}{2}}}$

Step 5.6.4.2

Rewrite the expression.

$\frac{\sqrt{5 x} \sqrt{y}}{y^{1}}$

Step 5.6.5

Simplify.

$\frac{\sqrt{5 x} \sqrt{y}}{y}$

Step 6

Combine using the product rule for radicals.

$\frac{\sqrt{5 x y}}{y}$