Pre-Algebra Examples

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

Step 1

Pull out imaginary unit $i$ .

Tap for more steps...

Step 1.1

Rewrite $- 6$ as $- 1 (6)$ .

$\frac{\sqrt{- 1 (6)} \sqrt{- 3}}{\sqrt{2}}$

Step 1.2

Rewrite $\sqrt{- 1 (6)}$ as $\sqrt{- 1} \cdot \sqrt{6}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{6} \sqrt{- 3}}{\sqrt{2}}$

Step 1.3

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

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

Step 1.4

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{i \cdot \sqrt{6} \sqrt{- 1 (3)}}{\sqrt{2}}$

Step 1.5

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$\frac{i \cdot \sqrt{6} (\sqrt{- 1} \cdot \sqrt{3})}{\sqrt{2}}$

Step 1.6

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

$\frac{i \cdot \sqrt{6} (i \cdot \sqrt{3})}{\sqrt{2}}$

Step 2

Combine $\sqrt{6}$ and $\sqrt{2}$ into a single radical.

$i \cdot \sqrt{\frac{6}{2}} i \cdot \sqrt{3}$

Step 3

Divide $6$ by $2$ .

$i \cdot \sqrt{3} i \cdot \sqrt{3}$

Step 4

Multiply $i \sqrt{3} i$ .

Tap for more steps...

Step 4.1

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

$i^{1} i \sqrt{3} \cdot \sqrt{3}$

Step 4.2

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

$i^{1} i^{1} \sqrt{3} \cdot \sqrt{3}$

Step 4.3

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

$i^{1 + 1} \sqrt{3} \cdot \sqrt{3}$

Step 4.4

Add $1$ and $1$ .

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

Step 5

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

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

Step 6

Rewrite $- 1 \sqrt{3}$ as $- \sqrt{3}$ .

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

Step 7

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

Tap for more steps...

Step 7.1

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

$- ({\sqrt{3}}^{1} \sqrt{3})$

Step 7.2

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

$- ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

Step 7.3

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

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

Step 7.4

Add $1$ and $1$ .

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

Step 8

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

Tap for more steps...

Step 8.1

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

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

Step 8.2

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

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

Step 8.3

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

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

Step 8.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 8.4.1

Cancel the common factor.

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

Step 8.4.2

Rewrite the expression.

$- 3^{1}$

Step 8.5

Evaluate the exponent.

$- 1 \cdot 3$

Step 9

Multiply $- 1$ by $3$ .

$- 3$