Basic Math Examples

$\frac{15}{\sqrt{5}}$

Step 1

Multiply

$\frac{15}{\sqrt{5}}$ by

$\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{15}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply

$\frac{15}{\sqrt{5}}$ by

$\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{15 \sqrt{5}}{\sqrt{5} \sqrt{5}}$

Step 2.2

Raise

$\sqrt{5}$ to the power of

$1$ .

$\frac{15 \sqrt{5}}{{\sqrt{5}}^{1} \sqrt{5}}$

Step 2.3

Raise

$\sqrt{5}$ to the power of

$1$ .

$\frac{15 \sqrt{5}}{{\sqrt{5}}^{1} {\sqrt{5}}^{1}}$

Step 2.4

Use the power rule

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

$\frac{15 \sqrt{5}}{{\sqrt{5}}^{1 + 1}}$

Step 2.5

Add

$1$ and

$1$ .

$\frac{15 \sqrt{5}}{{\sqrt{5}}^{2}}$

Step 2.6

Rewrite

${\sqrt{5}}^{2}$ as

$5$ .

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Step 2.6.1

Use

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

$\sqrt{5}$ as

$5^{\frac{1}{2}}$ .

$\frac{15 \sqrt{5}}{{(5^{\frac{1}{2}})}^{2}}$

Step 2.6.2

Apply the power rule and multiply exponents,

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

$\frac{15 \sqrt{5}}{5^{\frac{1}{2} \cdot 2}}$

Step 2.6.3

Combine

$\frac{1}{2}$ and

$2$ .

$\frac{15 \sqrt{5}}{5^{\frac{2}{2}}}$

Step 2.6.4

Cancel the common factor of

$2$ .

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Step 2.6.4.1

Cancel the common factor.

$\frac{15 \sqrt{5}}{5^{\frac{2}{2}}}$

Step 2.6.4.2

Rewrite the expression.

$\frac{15 \sqrt{5}}{5^{1}}$

$\frac{15 \sqrt{5}}{5^{1}}$

Step 2.6.5

Evaluate the exponent.

$\frac{15 \sqrt{5}}{5}$

$\frac{15 \sqrt{5}}{5}$

$\frac{15 \sqrt{5}}{5}$

Step 3

Cancel the common factor of

$15$ and

$5$ .

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Step 3.1

Factor

$5$ out of

$15 \sqrt{5}$ .

$\frac{5 (3 \sqrt{5})}{5}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor

$5$ out of

$5$ .

$\frac{5 (3 \sqrt{5})}{5 (1)}$

Step 3.2.2

Cancel the common factor.

$\frac{5 (3 \sqrt{5})}{5 \cdot 1}$

Step 3.2.3

Rewrite the expression.

$\frac{3 \sqrt{5}}{1}$

Step 3.2.4

Divide

$3 \sqrt{5}$ by

$1$ .

$3 \sqrt{5}$

$3 \sqrt{5}$

$3 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{5}$

Decimal Form:

$6.70820393 \dots$

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