Simplify (9-6 square root of 2)/( square root of 30)

$\frac{9 - 6 \sqrt{2}}{\sqrt{30}}$

Multiply $\frac{9 - 6 \sqrt{2}}{\sqrt{30}}$ by $\frac{\sqrt{30}}{\sqrt{30}}$ .

$\frac{9 - 6 \sqrt{2}}{\sqrt{30}} \cdot \frac{\sqrt{30}}{\sqrt{30}}$

Combine and simplify the denominator.

Multiply $\frac{9 - 6 \sqrt{2}}{\sqrt{30}}$ by $\frac{\sqrt{30}}{\sqrt{30}}$ .

$\frac{(9 - 6 \sqrt{2}) \sqrt{30}}{\sqrt{30} \sqrt{30}}$

Raise $\sqrt{30}$ to the power of $1$ .

$\frac{(9 - 6 \sqrt{2}) \sqrt{30}}{{\sqrt{30}}^{1} \sqrt{30}}$

Raise $\sqrt{30}$ to the power of $1$ .

$\frac{(9 - 6 \sqrt{2}) \sqrt{30}}{{\sqrt{30}}^{1} {\sqrt{30}}^{1}}$

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

$\frac{(9 - 6 \sqrt{2}) \sqrt{30}}{{\sqrt{30}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{(9 - 6 \sqrt{2}) \sqrt{30}}{{\sqrt{30}}^{2}}$

Rewrite ${\sqrt{30}}^{2}$ as $30$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{30}$ as $30^{\frac{1}{2}}$ .

$\frac{(9 - 6 \sqrt{2}) \sqrt{30}}{{(30^{\frac{1}{2}})}^{2}}$

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

$\frac{(9 - 6 \sqrt{2}) \sqrt{30}}{30^{\frac{1}{2} \cdot 2}}$

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

$\frac{(9 - 6 \sqrt{2}) \sqrt{30}}{30^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{(9 - 6 \sqrt{2}) \sqrt{30}}{30^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{(9 - 6 \sqrt{2}) \sqrt{30}}{30^{1}}$

Evaluate the exponent.

$\frac{(9 - 6 \sqrt{2}) \sqrt{30}}{30}$

Cancel the common factor of $9 - 6 \sqrt{2}$ and $30$ .

Factor $3$ out of $(9 - 6 \sqrt{2}) \sqrt{30}$ .

$\frac{3 ((3 - 2 \sqrt{2}) \sqrt{30})}{30}$

Cancel the common factors.

Factor $3$ out of $30$ .

$\frac{3 ((3 - 2 \sqrt{2}) \sqrt{30})}{3 (10)}$

Cancel the common factor.

$\frac{3 ((3 - 2 \sqrt{2}) \sqrt{30})}{3 \cdot 10}$

Rewrite the expression.

$\frac{(3 - 2 \sqrt{2}) \sqrt{30}}{10}$

Apply the distributive property.

$\frac{3 \sqrt{30} - 2 \sqrt{2} \sqrt{30}}{10}$

Multiply $- 2 \sqrt{2} \sqrt{30}$ .

Combine using the product rule for radicals.

$\frac{3 \sqrt{30} - 2 \sqrt{30 \cdot 2}}{10}$

Multiply $30$ by $2$ .

$\frac{3 \sqrt{30} - 2 \sqrt{60}}{10}$

Simplify each term.

Rewrite $60$ as $2^{2} \cdot 15$ .

Factor $4$ out of $60$ .

$\frac{3 \sqrt{30} - 2 \sqrt{4 (15)}}{10}$

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

$\frac{3 \sqrt{30} - 2 \sqrt{2^{2} \cdot 15}}{10}$

Pull terms out from under the radical.

$\frac{3 \sqrt{30} - 2 (2 \sqrt{15})}{10}$

Multiply $2$ by $- 2$ .

$\frac{3 \sqrt{30} - 4 \sqrt{15}}{10}$

The result can be shown in multiple forms.

Exact Form:

$\frac{3 \sqrt{30} - 4 \sqrt{15}}{10}$

Decimal Form:

$0.09397433 \dots$

Simplify (9-6 square root of 2)/( square root of 30)

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