Simplify square root of -5* square root of -10

$\sqrt{- 5} \cdot \sqrt{- 10}$

Step 1

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

$\sqrt{- 1 (5)} \cdot \sqrt{- 10}$

Step 2

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

$\sqrt{- 1} \cdot \sqrt{5} \cdot \sqrt{- 10}$

Step 3

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

$i \cdot \sqrt{5} \cdot \sqrt{- 10}$

Step 4

Rewrite $- 10$ as $- 1 (10)$ .

$i \cdot \sqrt{5} \cdot \sqrt{- 1 (10)}$

Step 5

Rewrite $\sqrt{- 1 (10)}$ as $\sqrt{- 1} \cdot \sqrt{10}$ .

$i \cdot \sqrt{5} \cdot (\sqrt{- 1} \cdot \sqrt{10})$

Step 6

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

$i \cdot \sqrt{5} \cdot (i \cdot \sqrt{10})$

Step 7

Multiply $i \sqrt{5} (i \sqrt{10})$ .

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

$i^{1} i \sqrt{5} \sqrt{10}$

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

$i^{1} i^{1} \sqrt{5} \sqrt{10}$

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

$i^{1 + 1} \sqrt{5} \sqrt{10}$

Add $1$ and $1$ .

$i^{2} \sqrt{5} \sqrt{10}$

Combine using the product rule for radicals.

$i^{2} \sqrt{10 \cdot 5}$

Multiply $10$ by $5$ .

$i^{2} \sqrt{50}$

Step 8

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

$- 1 \sqrt{50}$

Step 9

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$- 1 \sqrt{25 (2)}$

Rewrite $25$ as $5^{2}$ .

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

Step 10

Pull terms out from under the radical.

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

Step 11

Multiply $5$ by $- 1$ .

$- 5 \sqrt{2}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$- 5 \sqrt{2}$

Decimal Form:

$- 7.07106781 \dots$

Simplify square root of -5* square root of -10

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