Simplify square root of -18*3 square root of -8

$\sqrt{- 18} \cdot 3 \sqrt{- 8}$

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

$\sqrt{- 1 (18)} \cdot (3 \sqrt{- 8})$

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

$\sqrt{- 1} \cdot \sqrt{18} \cdot (3 \sqrt{- 8})$

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

$i \cdot \sqrt{18} \cdot (3 \sqrt{- 8})$

Rewrite $- 8$ as $- 1 (8)$ .

$i \cdot \sqrt{18} \cdot (3 \sqrt{- 1 (8)})$

Rewrite $\sqrt{- 1 (8)}$ as $\sqrt{- 1} \cdot \sqrt{8}$ .

$i \cdot \sqrt{18} \cdot (3 (\sqrt{- 1} \cdot \sqrt{8}))$

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

$i \cdot \sqrt{18} \cdot (3 (i \cdot \sqrt{8}))$

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

Factor $9$ out of $18$ .

$i \cdot \sqrt{9 (2)} \cdot (3 (i \cdot \sqrt{8}))$

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

$i \cdot \sqrt{3^{2} \cdot 2} \cdot (3 (i \cdot \sqrt{8}))$

Pull terms out from under the radical.

$i \cdot (3 \sqrt{2}) \cdot (3 (i \cdot \sqrt{8}))$

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

$3 \cdot i \sqrt{2} \cdot (3 (i \cdot \sqrt{8}))$

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$3 i \sqrt{2} \cdot (3 (i \cdot \sqrt{4 (2)}))$

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

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

Pull terms out from under the radical.

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

Simplify the expression.

Move $2$ to the left of $i$ .

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

Multiply $2$ by $3$ .

$3 i \sqrt{2} \cdot (6 (i \sqrt{2}))$

Multiply $3 i \sqrt{2} (6 i \sqrt{2})$ .

Multiply $6$ by $3$ .

$18 i \sqrt{2} (i \sqrt{2})$

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

$18 (i^{1} i) \sqrt{2} \sqrt{2}$

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

$18 (i^{1} i^{1}) \sqrt{2} \sqrt{2}$

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

$18 i^{1 + 1} \sqrt{2} \sqrt{2}$

Add $1$ and $1$ .

$18 i^{2} \sqrt{2} \sqrt{2}$

Raise $\sqrt{2}$ to the power of $1$ .

$18 i^{2} ({\sqrt{2}}^{1} \sqrt{2})$

Raise $\sqrt{2}$ to the power of $1$ .

$18 i^{2} ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

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

$18 i^{2} {\sqrt{2}}^{1 + 1}$

Add $1$ and $1$ .

$18 i^{2} {\sqrt{2}}^{2}$

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

$18 \cdot - 1 {\sqrt{2}}^{2}$

Multiply $18$ by $- 1$ .

$- 18 {\sqrt{2}}^{2}$

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$- 18 {(2^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 18 \cdot 2^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$- 18 \cdot 2^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 18 \cdot 2^{\frac{2}{2}}$

Rewrite the expression.

$- 18 \cdot 2^{1}$

Evaluate the exponent.

$- 18 \cdot 2$

Multiply $- 18$ by $2$ .

$- 36$

Simplify square root of -18*3 square root of -8

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