Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

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

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

Pull out imaginary unit $i$ .

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 3

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

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

Step 4

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

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Step 4.1

Factor $6$ out of $6$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $6$ out of $12$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Multiply $i i$ .

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Step 5.1

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

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

Step 5.2

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

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

Step 5.3

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

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

Step 5.4

Add $1$ and $1$ .

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

Step 6

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

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

Step 7

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

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

Step 8

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

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

Step 9

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

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

Step 10

Any root of $1$ is $1$ .

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

Step 11

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

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

Step 12

Combine and simplify the denominator.

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Step 12.1

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

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

Step 12.2

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

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

Step 12.3

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

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

Step 12.4

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

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

Step 12.5

Add $1$ and $1$ .

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

Step 12.6

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

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Step 12.6.1

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

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

Step 12.6.2

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

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

Step 12.6.3

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

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

Step 12.6.4

Cancel the common factor of $2$ .

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Step 12.6.4.1

Cancel the common factor.

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

Step 12.6.4.2

Rewrite the expression.

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

Step 12.6.5

Evaluate the exponent.

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

Step 13

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

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

Step 14

Move the negative in front of the fraction.

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

Step 15

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

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Step 15.1

Multiply $- 1$ by $- 1$ .

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

Step 15.2

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

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

Step 16

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$3.53553390 \dots$