Evaluate square root of 3( square root of 12-2)

$\sqrt{3} (\sqrt{12} - 2)$

Step 1

Simplify each term.

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

Factor $4$ out of $12$ .

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

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

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

Pull terms out from under the radical.

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

Step 2

Apply the distributive property.

$\sqrt{3} (2 \sqrt{3}) + \sqrt{3} \cdot - 2$

Step 3

Multiply $\sqrt{3} (2 \sqrt{3})$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

Step 4

Move $- 2$ to the left of $\sqrt{3}$ .

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

Step 5

Simplify each term.

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Multiply $2$ by $3$ .

$6 - 2 \sqrt{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$6 - 2 \sqrt{3}$

Decimal Form:

$2.53589838 \dots$

Evaluate square root of 3( square root of 12-2)

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