Simplify (-35 square root of 6)/(7i square root of -12)

$\frac{- 35 \sqrt{6}}{7 i \sqrt{- 12}}$

Cancel the common factor of $- 35$ and $7$ .

Factor $7$ out of $- 35 \sqrt{6}$ .

$\frac{7 (- 5 \sqrt{6})}{7 i \sqrt{- 12}}$

Cancel the common factors.

Factor $7$ out of $7 i \sqrt{- 12}$ .

$\frac{7 (- 5 \sqrt{6})}{7 (i \sqrt{- 12})}$

Cancel the common factor.

$\frac{7 (- 5 \sqrt{6})}{7 (i \sqrt{- 12})}$

Rewrite the expression.

$\frac{- 5 \sqrt{6}}{i \sqrt{- 12}}$

Pull out imaginary unit $i$ .

Rewrite $- 12$ as $- 1 (12)$ .

$\frac{- 5 \sqrt{6}}{i \sqrt{- 1 (12)}}$

Rewrite $\sqrt{- 1 (12)}$ as $\sqrt{- 1} \cdot \sqrt{12}$ .

$\frac{- 5 \sqrt{6}}{i (\sqrt{- 1} \cdot \sqrt{12})}$

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{- 5 \sqrt{6}}{i (i \cdot \sqrt{12})}$

Combine $\sqrt{6}$ and $\sqrt{12}$ into a single radical.

$\frac{- 5 \sqrt{\frac{6}{12}}}{i i}$

Cancel the common factor of $6$ and $12$ .

Factor $6$ out of $6$ .

$\frac{- 5 \sqrt{\frac{6 (1)}{12}}}{i i}$

Cancel the common factors.

Factor $6$ out of $12$ .

$\frac{- 5 \sqrt{\frac{6 \cdot 1}{6 \cdot 2}}}{i i}$

Cancel the common factor.

$\frac{- 5 \sqrt{\frac{6 \cdot 1}{6 \cdot 2}}}{i i}$

Rewrite the expression.

$\frac{- 5 \sqrt{\frac{1}{2}}}{i i}$

Multiply $i i$ .

Raise $i$ to the power of $1$ .

$\frac{- 5 \sqrt{\frac{1}{2}}}{i^{1} i}$

Raise $i$ to the power of $1$ .

$\frac{- 5 \sqrt{\frac{1}{2}}}{i^{1} i^{1}}$

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

$\frac{- 5 \sqrt{\frac{1}{2}}}{i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{- 5 \sqrt{\frac{1}{2}}}{i^{2}}$

Rewrite $i^{2}$ as $- 1$ .

$\frac{- 5 \sqrt{\frac{1}{2}}}{- 1}$

Move the negative one from the denominator of $\frac{- 5 \sqrt{\frac{1}{2}}}{- 1}$ .

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

Rewrite $- 1 \cdot (- 5 \sqrt{\frac{1}{2}})$ as $- (- 5 \sqrt{\frac{1}{2}})$ .

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

Rewrite $\sqrt{\frac{1}{2}}$ as $\frac{\sqrt{1}}{\sqrt{2}}$ .

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

Any root of $1$ is $1$ .

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

Multiply $\frac{1}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Raise $\sqrt{2}$ to the power of $1$ .

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

Raise $\sqrt{2}$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Combine $- 5$ and $\frac{\sqrt{2}}{2}$ .

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

Move the negative in front of the fraction.

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

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

Multiply $- 1$ by $- 1$ .

$1 \frac{5 \sqrt{2}}{2}$

Multiply $\frac{5 \sqrt{2}}{2}$ by $1$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$3.53553390 \dots$

Simplify (-35 square root of 6)/(7i square root of -12)

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