Simplify square root of -18* square root of -10

$\sqrt{- 18} \cdot \sqrt{- 10}$

Rewrite $- 18$ as $- 1 (18)$ .

$\sqrt{- 1 (18)} \cdot \sqrt{- 10}$

Rewrite $\sqrt{- 1 (18)}$ as $\sqrt{- 1} \cdot \sqrt{18}$ .

$\sqrt{- 1} \cdot \sqrt{18} \cdot \sqrt{- 10}$

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

$i \cdot \sqrt{18} \cdot \sqrt{- 10}$

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

$i \cdot \sqrt{18} \cdot \sqrt{- 1 (10)}$

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

$i \cdot \sqrt{18} \cdot (\sqrt{- 1} \cdot \sqrt{10})$

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

$i \cdot \sqrt{18} \cdot (i \cdot \sqrt{10})$

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$i \cdot \sqrt{9 (2)} \cdot (i \cdot \sqrt{10})$

Rewrite $9$ as $3^{2}$ .

$i \cdot \sqrt{3^{2} \cdot 2} \cdot (i \cdot \sqrt{10})$

Pull terms out from under the radical.

$i \cdot (3 \sqrt{2}) \cdot (i \cdot \sqrt{10})$

Move $3$ to the left of $i$ .

$3 \cdot i \sqrt{2} \cdot (i \cdot \sqrt{10})$

Multiply $3 i \sqrt{2} (i \sqrt{10})$ .

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

$3 (i^{1} i) \sqrt{2} \sqrt{10}$

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

$3 (i^{1} i^{1}) \sqrt{2} \sqrt{10}$

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

$3 i^{1 + 1} \sqrt{2} \sqrt{10}$

Add $1$ and $1$ .

$3 i^{2} \sqrt{2} \sqrt{10}$

Combine using the product rule for radicals.

$3 i^{2} \sqrt{10 \cdot 2}$

Multiply $10$ by $2$ .

$3 i^{2} \sqrt{20}$

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

$3 \cdot - 1 \sqrt{20}$

Multiply $3$ by $- 1$ .

$- 3 \sqrt{20}$

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$- 3 \sqrt{4 (5)}$

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 3$ .

$- 6 \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$- 6 \sqrt{5}$

Decimal Form:

$- 13.41640786 \dots$

Simplify square root of -18* square root of -10

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