Basic Math Examples

\frac{16}{\sqrt{12}}

$\frac{16}{\sqrt{12}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite

12

$12$ as

2^{2} \cdot 3

$2^{2} \cdot 3$ .

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Step 1.1.1

Factor

4

$4$ out of

12

$12$ .

\frac{16}{\sqrt{4 (3)}}

$\frac{16}{\sqrt{4 (3)}}$

Step 1.1.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

\frac{16}{\sqrt{2^{2} \cdot 3}}

$\frac{16}{\sqrt{2^{2} \cdot 3}}$

\frac{16}{\sqrt{2^{2} \cdot 3}}

$\frac{16}{\sqrt{2^{2} \cdot 3}}$

Step 1.2

Pull terms out from under the radical.

\frac{16}{2 \sqrt{3}}

$\frac{16}{2 \sqrt{3}}$

\frac{16}{2 \sqrt{3}}

$\frac{16}{2 \sqrt{3}}$

Step 2

Cancel the common factor of

16

$16$ and

2

$2$ .

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Step 2.1

Factor

2

$2$ out of

16

$16$ .

\frac{2 \cdot 8}{2 \sqrt{3}}

$\frac{2 \cdot 8}{2 \sqrt{3}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor

2

$2$ out of

2 \sqrt{3}

$2 \sqrt{3}$ .

\frac{2 \cdot 8}{2 (\sqrt{3})}

$\frac{2 \cdot 8}{2 (\sqrt{3})}$

Step 2.2.2

Cancel the common factor.

$\frac{2 \cdot 8}{2 \sqrt{3}}$

Step 2.2.3

Rewrite the expression.

$\frac{8}{\sqrt{3}}$

$\frac{8}{\sqrt{3}}$

$\frac{8}{\sqrt{3}}$

Step 3

Multiply

$\frac{8}{\sqrt{3}}$ by

$\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{8}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply

$\frac{8}{\sqrt{3}}$ by

$\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{8 \sqrt{3}}{\sqrt{3} \sqrt{3}}$

Step 4.2

Raise

$\sqrt{3}$ to the power of

$1$ .

$\frac{8 \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

Step 4.3

Raise

$\sqrt{3}$ to the power of

$1$ .

$\frac{8 \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

Step 4.4

Use the power rule

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

$\frac{8 \sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Step 4.5

Add

$1$ and

$1$ .

$\frac{8 \sqrt{3}}{{\sqrt{3}}^{2}}$

Step 4.6

Rewrite

${\sqrt{3}}^{2}$ as

$3$ .

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Step 4.6.1

Use

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

$\sqrt{3}$ as

$3^{\frac{1}{2}}$ .

$\frac{8 \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}$

Step 4.6.2

Apply the power rule and multiply exponents,

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

$\frac{8 \sqrt{3}}{3^{\frac{1}{2} \cdot 2}}$

Step 4.6.3

Combine

$\frac{1}{2}$ and

$2$ .

$\frac{8 \sqrt{3}}{3^{\frac{2}{2}}}$

Step 4.6.4

Cancel the common factor of

$2$ .

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Step 4.6.4.1

Cancel the common factor.

$\frac{8 \sqrt{3}}{3^{\frac{2}{2}}}$

Step 4.6.4.2

Rewrite the expression.

$\frac{8 \sqrt{3}}{3^{1}}$

$\frac{8 \sqrt{3}}{3^{1}}$

Step 4.6.5

Evaluate the exponent.

$\frac{8 \sqrt{3}}{3}$

$\frac{8 \sqrt{3}}{3}$

$\frac{8 \sqrt{3}}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{8 \sqrt{3}}{3}$

Decimal Form:

$4.61880215 \dots$

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