Algebra Examples

\frac{5}{\sqrt{10}}

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

Step 1

Multiply

\frac{5}{\sqrt{10}}

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

\frac{\sqrt{10}}{\sqrt{10}}

$\frac{\sqrt{10}}{\sqrt{10}}$ .

\frac{5}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}

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

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply

\frac{5}{\sqrt{10}}

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

\frac{\sqrt{10}}{\sqrt{10}}

$\frac{\sqrt{10}}{\sqrt{10}}$ .

\frac{5 \sqrt{10}}{\sqrt{10} \sqrt{10}}

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

Step 2.2

Raise

\sqrt{10}

$\sqrt{10}$ to the power of

1

$1$ .

\frac{5 \sqrt{10}}{{\sqrt{10}}^{1} \sqrt{10}}

$\frac{5 \sqrt{10}}{{\sqrt{10}}^{1} \sqrt{10}}$

Step 2.3

Raise

\sqrt{10}

$\sqrt{10}$ to the power of

1

$1$ .

\frac{5 \sqrt{10}}{{\sqrt{10}}^{1} {\sqrt{10}}^{1}}

$\frac{5 \sqrt{10}}{{\sqrt{10}}^{1} {\sqrt{10}}^{1}}$

Step 2.4

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

\frac{5 \sqrt{10}}{{\sqrt{10}}^{1 + 1}}

$\frac{5 \sqrt{10}}{{\sqrt{10}}^{1 + 1}}$

Step 2.5

Add

1

$1$ and

1

$1$ .

\frac{5 \sqrt{10}}{{\sqrt{10}}^{2}}

$\frac{5 \sqrt{10}}{{\sqrt{10}}^{2}}$

Step 2.6

Rewrite

{\sqrt{10}}^{2}

${\sqrt{10}}^{2}$ as

10

$10$ .

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Step 2.6.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{10}

$\sqrt{10}$ as

10^{\frac{1}{2}}

$10^{\frac{1}{2}}$ .

\frac{5 \sqrt{10}}{{(10^{\frac{1}{2}})}^{2}}

$\frac{5 \sqrt{10}}{{(10^{\frac{1}{2}})}^{2}}$

Step 2.6.2

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

\frac{5 \sqrt{10}}{10^{\frac{1}{2} \cdot 2}}

$\frac{5 \sqrt{10}}{10^{\frac{1}{2} \cdot 2}}$

Step 2.6.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

\frac{5 \sqrt{10}}{10^{\frac{2}{2}}}

$\frac{5 \sqrt{10}}{10^{\frac{2}{2}}}$

Step 2.6.4

Cancel the common factor of

2

$2$ .

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Step 2.6.4.1

Cancel the common factor.

$\frac{5 \sqrt{10}}{10^{\frac{2}{2}}}$

Step 2.6.4.2

Rewrite the expression.

$\frac{5 \sqrt{10}}{10^{1}}$

$\frac{5 \sqrt{10}}{10^{1}}$

Step 2.6.5

Evaluate the exponent.

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

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

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

Step 3

Cancel the common factor of

$5$ and

$10$ .

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Step 3.1

Factor

$5$ out of

$5 \sqrt{10}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor

$5$ out of

$10$ .

$\frac{5 \sqrt{10}}{5 \cdot 2}$

Step 3.2.2

Cancel the common factor.

$\frac{5 \sqrt{10}}{5 \cdot 2}$

Step 3.2.3

Rewrite the expression.

$\frac{\sqrt{10}}{2}$

$\frac{\sqrt{10}}{2}$

$\frac{\sqrt{10}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{10}}{2}$

Decimal Form:

$1.58113883 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$