Evaluate square root of -25* square root of -16

$\sqrt{- 25} \cdot \sqrt{- 16}$

Step 1

Rewrite $- 25$ as $- 1 (25)$ .

$\sqrt{- 1 (25)} \cdot \sqrt{- 16}$

Step 2

Rewrite $\sqrt{- 1 (25)}$ as $\sqrt{- 1} \cdot \sqrt{25}$ .

$\sqrt{- 1} \cdot \sqrt{25} \cdot \sqrt{- 16}$

Step 3

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

$i \cdot \sqrt{25} \cdot \sqrt{- 16}$

Step 4

Rewrite $- 16$ as $- 1 (16)$ .

$i \cdot \sqrt{25} \cdot \sqrt{- 1 (16)}$

Step 5

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$i \cdot \sqrt{25} \cdot (\sqrt{- 1} \cdot \sqrt{16})$

Step 6

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

$i \cdot \sqrt{25} \cdot (i \cdot \sqrt{16})$

Step 7

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

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

Step 8

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

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

Step 9

Move $5$ to the left of $i$ .

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

Step 10

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

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

Step 11

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

$5 i \cdot (i \cdot 4)$

Step 12

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

$5 i \cdot (4 \cdot i)$

Step 13

Multiply $5 i (4 i)$ .

Multiply $4$ by $5$ .

$20 i i$

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

$20 (i^{1} i)$

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

$20 (i^{1} i^{1})$

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

$20 i^{1 + 1}$

Add $1$ and $1$ .

$20 i^{2}$

Step 14

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

$20 \cdot - 1$

Step 15

Multiply $20$ by $- 1$ .

$- 20$

Evaluate square root of -25* square root of -16

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