Simplify (9 square root of -64)(- square root of -5)

$(9 \sqrt{- 64}) (- \sqrt{- 5})$

Step 1

Rewrite $- 64$ as $- 1 (64)$ .

$9 \sqrt{- 1 (64)} (- \sqrt{- 5})$

Step 2

Rewrite $\sqrt{- 1 (64)}$ as $\sqrt{- 1} \cdot \sqrt{64}$ .

$9 (\sqrt{- 1} \cdot \sqrt{64}) (- \sqrt{- 5})$

Step 3

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

$9 (i \cdot \sqrt{64}) (- \sqrt{- 5})$

Step 4

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

$9 (i \cdot \sqrt{64}) (- \sqrt{- 1 (5)})$

Step 5

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

$9 (i \cdot \sqrt{64}) (- (\sqrt{- 1} \cdot \sqrt{5}))$

Step 6

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

$9 (i \cdot \sqrt{64}) (- (i \cdot \sqrt{5}))$

Step 7

Rewrite $64$ as $8^{2}$ .

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

Step 8

Pull terms out from under the radical, assuming positive real numbers.

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

Step 9

Move $8$ to the left of $i$ .

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

Step 10

Multiply $8$ by $9$ .

$72 i (- (i \cdot \sqrt{5}))$

Step 11

Multiply $72 i (- i \sqrt{5})$ .

Multiply $- 1$ by $72$ .

$- 72 i (i \sqrt{5})$

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

$- 72 (i^{1} i) \sqrt{5}$

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

$- 72 (i^{1} i^{1}) \sqrt{5}$

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

$- 72 i^{1 + 1} \sqrt{5}$

Add $1$ and $1$ .

$- 72 i^{2} \sqrt{5}$

Step 12

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

$- 72 \cdot - 1 \sqrt{5}$

Step 13

Multiply $- 72$ by $- 1$ .

$72 \sqrt{5}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$72 \sqrt{5}$

Decimal Form:

$160.99689437 \dots$

Simplify (9 square root of -64)(- square root of -5)

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