Simplify (2 square root of -32)(5 square root of -18)

$(2 \sqrt{- 32}) (5 \sqrt{- 18})$

Rewrite $- 32$ as $- 1 (32)$ .

$2 \sqrt{- 1 (32)} (5 \sqrt{- 18})$

Rewrite $\sqrt{- 1 (32)}$ as $\sqrt{- 1} \cdot \sqrt{32}$ .

$2 (\sqrt{- 1} \cdot \sqrt{32}) (5 \sqrt{- 18})$

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

$2 (i \cdot \sqrt{32}) (5 \sqrt{- 18})$

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

$2 (i \cdot \sqrt{32}) (5 \sqrt{- 1 (18)})$

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

$2 (i \cdot \sqrt{32}) (5 (\sqrt{- 1} \cdot \sqrt{18}))$

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

$2 (i \cdot \sqrt{32}) (5 (i \cdot \sqrt{18}))$

Rewrite $32$ as $4^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$2 (i \cdot \sqrt{16 (2)}) (5 (i \cdot \sqrt{18}))$

Rewrite $16$ as $4^{2}$ .

$2 (i \cdot \sqrt{4^{2} \cdot 2}) (5 (i \cdot \sqrt{18}))$

Pull terms out from under the radical.

$2 (i \cdot (4 \sqrt{2})) (5 (i \cdot \sqrt{18}))$

Simplify the expression.

Move $4$ to the left of $i$ .

$2 (4 \cdot i \sqrt{2}) (5 (i \cdot \sqrt{18}))$

Multiply $4$ by $2$ .

$8 (i \sqrt{2}) (5 (i \cdot \sqrt{18}))$

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

Factor $9$ out of $18$ .

$8 i \sqrt{2} (5 (i \cdot \sqrt{9 (2)}))$

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

$8 i \sqrt{2} (5 (i \cdot \sqrt{3^{2} \cdot 2}))$

Pull terms out from under the radical.

$8 i \sqrt{2} (5 (i \cdot (3 \sqrt{2})))$

Simplify the expression.

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

$8 i \sqrt{2} (5 (3 \cdot i \sqrt{2}))$

Multiply $3$ by $5$ .

$8 i \sqrt{2} (15 (i \sqrt{2}))$

Multiply $8 i \sqrt{2} (15 i \sqrt{2})$ .

Multiply $15$ by $8$ .

$120 i \sqrt{2} (i \sqrt{2})$

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

$120 (i^{1} i) \sqrt{2} \sqrt{2}$

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

$120 (i^{1} i^{1}) \sqrt{2} \sqrt{2}$

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

$120 i^{1 + 1} \sqrt{2} \sqrt{2}$

Add $1$ and $1$ .

$120 i^{2} \sqrt{2} \sqrt{2}$

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

$120 i^{2} ({\sqrt{2}}^{1} \sqrt{2})$

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

$120 i^{2} ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

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

$120 i^{2} {\sqrt{2}}^{1 + 1}$

Add $1$ and $1$ .

$120 i^{2} {\sqrt{2}}^{2}$

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

$120 \cdot - 1 {\sqrt{2}}^{2}$

Multiply $120$ by $- 1$ .

$- 120 {\sqrt{2}}^{2}$

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

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

$- 120 {(2^{\frac{1}{2}})}^{2}$

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

$- 120 \cdot 2^{\frac{1}{2} \cdot 2}$

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

$- 120 \cdot 2^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 120 \cdot 2^{\frac{2}{2}}$

Rewrite the expression.

$- 120 \cdot 2^{1}$

Evaluate the exponent.

$- 120 \cdot 2$

Multiply $- 120$ by $2$ .

$- 240$

Simplify (2 square root of -32)(5 square root of -18)

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