Basic Math Examples

$10 \div \sqrt{13}$

Step 1

Rewrite the division as a fraction.

$\frac{10}{\sqrt{13}}$

Step 2

Multiply

$\frac{10}{\sqrt{13}}$ by

$\frac{\sqrt{13}}{\sqrt{13}}$ .

$\frac{10}{\sqrt{13}} \cdot \frac{\sqrt{13}}{\sqrt{13}}$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply

$\frac{10}{\sqrt{13}}$ by

$\frac{\sqrt{13}}{\sqrt{13}}$ .

$\frac{10 \sqrt{13}}{\sqrt{13} \sqrt{13}}$

Step 3.2

Raise

$\sqrt{13}$ to the power of

$1$ .

$\frac{10 \sqrt{13}}{{\sqrt{13}}^{1} \sqrt{13}}$

Step 3.3

Raise

$\sqrt{13}$ to the power of

$1$ .

$\frac{10 \sqrt{13}}{{\sqrt{13}}^{1} {\sqrt{13}}^{1}}$

Step 3.4

Use the power rule

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

$\frac{10 \sqrt{13}}{{\sqrt{13}}^{1 + 1}}$

Step 3.5

Add

$1$ and

$1$ .

$\frac{10 \sqrt{13}}{{\sqrt{13}}^{2}}$

Step 3.6

Rewrite

${\sqrt{13}}^{2}$ as

$13$ .

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Step 3.6.1

Use

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

$\sqrt{13}$ as

$13^{\frac{1}{2}}$ .

$\frac{10 \sqrt{13}}{{(13^{\frac{1}{2}})}^{2}}$

Step 3.6.2

Apply the power rule and multiply exponents,

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

$\frac{10 \sqrt{13}}{13^{\frac{1}{2} \cdot 2}}$

Step 3.6.3

Combine

$\frac{1}{2}$ and

$2$ .

$\frac{10 \sqrt{13}}{13^{\frac{2}{2}}}$

Step 3.6.4

Cancel the common factor of

$2$ .

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Step 3.6.4.1

Cancel the common factor.

$\frac{10 \sqrt{13}}{13^{\frac{2}{2}}}$

Step 3.6.4.2

Rewrite the expression.

$\frac{10 \sqrt{13}}{13^{1}}$

$\frac{10 \sqrt{13}}{13^{1}}$

Step 3.6.5

Evaluate the exponent.

$\frac{10 \sqrt{13}}{13}$

$\frac{10 \sqrt{13}}{13}$

$\frac{10 \sqrt{13}}{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{10 \sqrt{13}}{13}$

Decimal Form:

$2.77350098 \dots$

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