Simplify (2- square root of 12)/( square root of 3)

$\frac{2 - \sqrt{12}}{\sqrt{3}}$

Simplify the numerator.

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

Factor $4$ out of $12$ .

$\frac{2 - \sqrt{4 (3)}}{\sqrt{3}}$

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 1$ .

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

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

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

Combine and simplify the denominator.

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Apply the distributive property.

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

Multiply $- 2 \sqrt{3} \sqrt{3}$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

Simplify each term.

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Multiply $- 2$ by $3$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 0.84529946 \dots$

Simplify (2- square root of 12)/( square root of 3)

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