Evaluate square root of -6* square root of -13

$\sqrt{- 6} \cdot \sqrt{- 13}$

Step 1

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

$\sqrt{- 1 (6)} \cdot \sqrt{- 13}$

Step 2

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

$\sqrt{- 1} \cdot \sqrt{6} \cdot \sqrt{- 13}$

Step 3

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

$i \cdot \sqrt{6} \cdot \sqrt{- 13}$

Step 4

Rewrite $- 13$ as $- 1 (13)$ .

$i \cdot \sqrt{6} \cdot \sqrt{- 1 (13)}$

Step 5

Rewrite $\sqrt{- 1 (13)}$ as $\sqrt{- 1} \cdot \sqrt{13}$ .

$i \cdot \sqrt{6} \cdot (\sqrt{- 1} \cdot \sqrt{13})$

Step 6

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

$i \cdot \sqrt{6} \cdot (i \cdot \sqrt{13})$

Step 7

Multiply $i \sqrt{6} (i \sqrt{13})$ .

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

$i^{1} i \sqrt{6} \sqrt{13}$

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

$i^{1} i^{1} \sqrt{6} \sqrt{13}$

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

$i^{1 + 1} \sqrt{6} \sqrt{13}$

Add $1$ and $1$ .

$i^{2} \sqrt{6} \sqrt{13}$

Combine using the product rule for radicals.

$i^{2} \sqrt{13 \cdot 6}$

Multiply $13$ by $6$ .

$i^{2} \sqrt{78}$

Step 8

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

$- 1 \sqrt{78}$

Step 9

Rewrite $- 1 \sqrt{78}$ as $- \sqrt{78}$ .

$- \sqrt{78}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{78}$

Decimal Form:

$- 8.83176086 \dots$