Basic Math Examples

$\frac{\sqrt{12}}{3 \sqrt{15}}$

Step 1

Combine $\sqrt{12}$ and $\sqrt{15}$ into a single radical.

$\frac{\sqrt{\frac{12}{15}}}{3}$

Step 2

Cancel the common factor of $12$ and $15$ .

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Step 2.1

Factor $3$ out of $12$ .

$\frac{\sqrt{\frac{3 (4)}{15}}}{3}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $15$ .

$\frac{\sqrt{\frac{3 \cdot 4}{3 \cdot 5}}}{3}$

Step 2.2.2

Cancel the common factor.

$\frac{\sqrt{\frac{3 \cdot 4}{3 \cdot 5}}}{3}$

Step 2.2.3

Rewrite the expression.

$\frac{\sqrt{\frac{4}{5}}}{3}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $\sqrt{\frac{4}{5}}$ as $\frac{\sqrt{4}}{\sqrt{5}}$ .

$\frac{\frac{\sqrt{4}}{\sqrt{5}}}{3}$

Step 3.2

Simplify the numerator.

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Step 3.2.1

Rewrite $4$ as $2^{2}$ .

$\frac{\frac{\sqrt{2^{2}}}{\sqrt{5}}}{3}$

Step 3.2.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{\frac{2}{\sqrt{5}}}{3}$

Step 3.3

Multiply $\frac{2}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{\frac{2}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}}{3}$

Step 3.4

Combine and simplify the denominator.

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Step 3.4.1

Multiply $\frac{2}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{\frac{2 \sqrt{5}}{\sqrt{5} \sqrt{5}}}{3}$

Step 3.4.2

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{\frac{2 \sqrt{5}}{{\sqrt{5}}^{1} \sqrt{5}}}{3}$

Step 3.4.3

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{\frac{2 \sqrt{5}}{{\sqrt{5}}^{1} {\sqrt{5}}^{1}}}{3}$

Step 3.4.4

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

$\frac{\frac{2 \sqrt{5}}{{\sqrt{5}}^{1 + 1}}}{3}$

Step 3.4.5

Add $1$ and $1$ .

$\frac{\frac{2 \sqrt{5}}{{\sqrt{5}}^{2}}}{3}$

Step 3.4.6

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

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Step 3.4.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$\frac{\frac{2 \sqrt{5}}{{(5^{\frac{1}{2}})}^{2}}}{3}$

Step 3.4.6.2

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

$\frac{\frac{2 \sqrt{5}}{5^{\frac{1}{2} \cdot 2}}}{3}$

Step 3.4.6.3

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

$\frac{\frac{2 \sqrt{5}}{5^{\frac{2}{2}}}}{3}$

Step 3.4.6.4

Cancel the common factor of $2$ .

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Step 3.4.6.4.1

Cancel the common factor.

$\frac{\frac{2 \sqrt{5}}{5^{\frac{2}{2}}}}{3}$

Step 3.4.6.4.2

Rewrite the expression.

$\frac{\frac{2 \sqrt{5}}{5^{1}}}{3}$

Step 3.4.6.5

Evaluate the exponent.

$\frac{\frac{2 \sqrt{5}}{5}}{3}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{2 \sqrt{5}}{5} \cdot \frac{1}{3}$

Step 5

Multiply $\frac{2 \sqrt{5}}{5} \cdot \frac{1}{3}$ .

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Step 5.1

Multiply $\frac{2 \sqrt{5}}{5}$ by $\frac{1}{3}$ .

$\frac{2 \sqrt{5}}{5 \cdot 3}$

Step 5.2

Multiply $5$ by $3$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.29814239 \dots$