Simplify (5-2 square root of 2)/( square root of 12)

$\frac{5 - 2 \sqrt{2}}{\sqrt{12}}$

Simplify the denominator.

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

Factor $4$ out of $12$ .

$\frac{5 - 2 \sqrt{2}}{\sqrt{4 (3)}}$

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

$\frac{5 - 2 \sqrt{2}}{\sqrt{2^{2} \cdot 3}}$

Pull terms out from under the radical.

$\frac{5 - 2 \sqrt{2}}{2 \sqrt{3}}$

Multiply $\frac{5 - 2 \sqrt{2}}{2 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{5 - 2 \sqrt{2}}{2 \sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

Combine and simplify the denominator.

Multiply $\frac{5 - 2 \sqrt{2}}{2 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{(5 - 2 \sqrt{2}) \sqrt{3}}{2 \sqrt{3} \sqrt{3}}$

Move $\sqrt{3}$ .

$\frac{(5 - 2 \sqrt{2}) \sqrt{3}}{2 (\sqrt{3} \sqrt{3})}$

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

$\frac{(5 - 2 \sqrt{2}) \sqrt{3}}{2 ({\sqrt{3}}^{1} \sqrt{3})}$

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

$\frac{(5 - 2 \sqrt{2}) \sqrt{3}}{2 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})}$

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

$\frac{(5 - 2 \sqrt{2}) \sqrt{3}}{2 {\sqrt{3}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{(5 - 2 \sqrt{2}) \sqrt{3}}{2 {\sqrt{3}}^{2}}$

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

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

$\frac{(5 - 2 \sqrt{2}) \sqrt{3}}{2 {(3^{\frac{1}{2}})}^{2}}$

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

$\frac{(5 - 2 \sqrt{2}) \sqrt{3}}{2 \cdot 3^{\frac{1}{2} \cdot 2}}$

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

$\frac{(5 - 2 \sqrt{2}) \sqrt{3}}{2 \cdot 3^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{(5 - 2 \sqrt{2}) \sqrt{3}}{2 \cdot 3^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{(5 - 2 \sqrt{2}) \sqrt{3}}{2 \cdot 3^{1}}$

Evaluate the exponent.

$\frac{(5 - 2 \sqrt{2}) \sqrt{3}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$\frac{(5 - 2 \sqrt{2}) \sqrt{3}}{6}$

Apply the distributive property.

$\frac{5 \sqrt{3} - 2 \sqrt{2} \sqrt{3}}{6}$

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

Combine using the product rule for radicals.

$\frac{5 \sqrt{3} - 2 \sqrt{3 \cdot 2}}{6}$

Multiply $3$ by $2$ .

$\frac{5 \sqrt{3} - 2 \sqrt{6}}{6}$

The result can be shown in multiple forms.

Exact Form:

$\frac{5 \sqrt{3} - 2 \sqrt{6}}{6}$

Decimal Form:

$0.62687909 \dots$

Simplify (5-2 square root of 2)/( square root of 12)

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