Simplify the Radical Expression 6/( square root of 12)

$\frac{6}{\sqrt{12}}$

Step 1

Simplify the denominator.

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

Factor $4$ out of $12$ .

$\frac{6}{\sqrt{4 (3)}}$

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

$\frac{6}{\sqrt{2^{2} \cdot 3}}$

Pull terms out from under the radical.

$\frac{6}{| 2 | \sqrt{3}}$

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

$\frac{6}{2 \sqrt{3}}$

Step 2

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $6$ .

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

Cancel the common factors.

Factor $2$ out of $2 \sqrt{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

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

Step 4

Combine and simplify the denominator.

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Step 5

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $\sqrt{3}$ by $1$ .

$\sqrt{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$

Simplify the Radical Expression 6/( square root of 12)

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