Algebra Examples

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

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

Rewrite $12$ as $2^{2} \cdot 3$ .

Tap for more steps...

Step 1.1.1

Factor $4$ out of $12$ .

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

Step 1.1.2

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

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

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

Step 2

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

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

Step 3

Combine and simplify the denominator.

Tap for more steps...

Step 3.1

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

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

Step 3.2

Move $\sqrt{3}$ .

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

Step 3.3

Raise $\sqrt{3}$ to the power of $1$ .

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

Step 3.4

Raise $\sqrt{3}$ to the power of $1$ .

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

Step 3.5

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

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

Step 3.6

Add $1$ and $1$ .

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

Step 3.7

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

Tap for more steps...

Step 3.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

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

Step 3.7.2

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

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

Step 3.7.3

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

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

Step 3.7.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.7.4.1

Cancel the common factor.

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

Step 3.7.4.2

Rewrite the expression.

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

Step 3.7.5

Evaluate the exponent.

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

Step 4

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.86602540 \dots$