Finite Math Examples

$\sqrt{\frac{5}{10 x}}$

Step 1

Reduce the expression $\frac{5}{10 x}$ by cancelling the common factors.

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Step 1.1

Factor $5$ out of $5$ .

$\sqrt{\frac{5 (1)}{10 x}}$

Step 1.2

Factor $5$ out of $10 x$ .

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

Step 1.3

Cancel the common factor.

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

Step 1.4

Rewrite the expression.

$\sqrt{\frac{1}{2 x}}$

Step 2

Rewrite $\sqrt{\frac{1}{2 x}}$ as $\frac{\sqrt{1}}{\sqrt{2 x}}$ .

$\frac{\sqrt{1}}{\sqrt{2 x}}$

Step 3

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{2 x}}$

Step 4

Multiply $\frac{1}{\sqrt{2 x}}$ by $\frac{\sqrt{2 x}}{\sqrt{2 x}}$ .

$\frac{1}{\sqrt{2 x}} \cdot \frac{\sqrt{2 x}}{\sqrt{2 x}}$

Step 5

Combine and simplify the denominator.

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Step 5.1

Multiply $\frac{1}{\sqrt{2 x}}$ by $\frac{\sqrt{2 x}}{\sqrt{2 x}}$ .

$\frac{\sqrt{2 x}}{\sqrt{2 x} \sqrt{2 x}}$

Step 5.2

Raise $\sqrt{2 x}$ to the power of $1$ .

$\frac{\sqrt{2 x}}{{\sqrt{2 x}}^{1} \sqrt{2 x}}$

Step 5.3

Raise $\sqrt{2 x}$ to the power of $1$ .

$\frac{\sqrt{2 x}}{{\sqrt{2 x}}^{1} {\sqrt{2 x}}^{1}}$

Step 5.4

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

$\frac{\sqrt{2 x}}{{\sqrt{2 x}}^{1 + 1}}$

Step 5.5

Add $1$ and $1$ .

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

Step 5.6

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

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Step 5.6.1

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

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

Step 5.6.2

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

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

Step 5.6.3

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

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

Step 5.6.4

Cancel the common factor of $2$ .

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Step 5.6.4.1

Cancel the common factor.

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

Step 5.6.4.2

Rewrite the expression.

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

Step 5.6.5

Simplify.

$\frac{\sqrt{2 x}}{2 x}$