Simplify square root of -6* square root of -2* square root of -5

$\sqrt{- 6} \cdot \sqrt{- 2} \cdot \sqrt{- 5}$

Step 1

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

$\sqrt{- 1 (6)} \cdot \sqrt{- 2} \cdot \sqrt{- 5}$

Step 2

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

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

Step 3

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

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

Step 4

Rewrite $- 2$ as $- 1 (2)$ .

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

Step 5

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

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

Step 6

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

$i \cdot \sqrt{6} \cdot (i \cdot \sqrt{2}) \cdot \sqrt{- 5}$

Step 7

Rewrite $- 5$ as $- 1 (5)$ .

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

Step 8

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

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

Step 9

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

$i \cdot \sqrt{6} \cdot (i \cdot \sqrt{2}) \cdot (i \cdot \sqrt{5})$

Step 10

Multiply $i \sqrt{6} (i \sqrt{2})$ .

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

$i^{1} i \sqrt{6} \sqrt{2} \cdot (i \cdot \sqrt{5})$

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

$i^{1} i^{1} \sqrt{6} \sqrt{2} \cdot (i \cdot \sqrt{5})$

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

$i^{1 + 1} \sqrt{6} \sqrt{2} \cdot (i \cdot \sqrt{5})$

Add $1$ and $1$ .

$i^{2} \sqrt{6} \sqrt{2} \cdot (i \cdot \sqrt{5})$

Combine using the product rule for radicals.

$i^{2} \sqrt{2 \cdot 6} \cdot (i \cdot \sqrt{5})$

Multiply $2$ by $6$ .

$i^{2} \sqrt{12} \cdot (i \cdot \sqrt{5})$

Step 11

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

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

Step 12

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$- 1 \sqrt{4 (3)} \cdot (i \cdot \sqrt{5})$

Rewrite $4$ as $2^{2}$ .

$- 1 \sqrt{2^{2} \cdot 3} \cdot (i \cdot \sqrt{5})$

Step 13

Pull terms out from under the radical.

$- 1 (2 \sqrt{3}) \cdot (i \cdot \sqrt{5})$

Step 14

Multiply $2$ by $- 1$ .

$- 2 \sqrt{3} \cdot (i \cdot \sqrt{5})$

Step 15

Multiply $- 2 \sqrt{3} (i \sqrt{5})$ .

Combine using the product rule for radicals.

$- 2 \sqrt{5 \cdot 3} i$

Multiply $5$ by $3$ .

$- 2 \sqrt{15} i$

Simplify square root of -6* square root of -2* square root of -5

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