Algebra Examples

$\sqrt{- 11} \cdot \sqrt{- 6}$

Step 1

Rewrite $- 11$ as $- 1 (11)$ .

$\sqrt{- 1 (11)} \cdot \sqrt{- 6}$

Step 2

Rewrite $\sqrt{- 1 (11)}$ as $\sqrt{- 1} \cdot \sqrt{11}$ .

$\sqrt{- 1} \cdot \sqrt{11} \cdot \sqrt{- 6}$

Step 3

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

$i \cdot \sqrt{11} \cdot \sqrt{- 6}$

Step 4

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

$i \cdot \sqrt{11} \cdot \sqrt{- 1 (6)}$

Step 5

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

$i \cdot \sqrt{11} \cdot (\sqrt{- 1} \cdot \sqrt{6})$

Step 6

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

$i \cdot \sqrt{11} \cdot (i \cdot \sqrt{6})$

Step 7

Multiply $i \sqrt{11} (i \sqrt{6})$ .

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Step 7.1

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

$i^{1} i \sqrt{11} \sqrt{6}$

Step 7.2

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

$i^{1} i^{1} \sqrt{11} \sqrt{6}$

Step 7.3

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

$i^{1 + 1} \sqrt{11} \sqrt{6}$

Step 7.4

Add $1$ and $1$ .

$i^{2} \sqrt{11} \sqrt{6}$

Step 7.5

Combine using the product rule for radicals.

$i^{2} \sqrt{6 \cdot 11}$

Step 7.6

Multiply $6$ by $11$ .

$i^{2} \sqrt{66}$

Step 8

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

$- 1 \sqrt{66}$

Step 9

Rewrite $- 1 \sqrt{66}$ as $- \sqrt{66}$ .

$- \sqrt{66}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{66}$

Decimal Form:

$- 8.12403840 \dots$