Evaluate square root of -81* square root of -16

$\sqrt{- 81} \cdot \sqrt{- 16}$

Step 1

Rewrite $- 81$ as $- 1 (81)$ .

$\sqrt{- 1 (81)} \cdot \sqrt{- 16}$

Step 2

Rewrite $\sqrt{- 1 (81)}$ as $\sqrt{- 1} \cdot \sqrt{81}$ .

$\sqrt{- 1} \cdot \sqrt{81} \cdot \sqrt{- 16}$

Step 3

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

$i \cdot \sqrt{81} \cdot \sqrt{- 16}$

Step 4

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

$i \cdot \sqrt{81} \cdot \sqrt{- 1 (16)}$

Step 5

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

$i \cdot \sqrt{81} \cdot (\sqrt{- 1} \cdot \sqrt{16})$

Step 6

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

$i \cdot \sqrt{81} \cdot (i \cdot \sqrt{16})$

Step 7

Rewrite $81$ as $9^{2}$ .

$i \cdot \sqrt{9^{2}} \cdot (i \cdot \sqrt{16})$

Step 8

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

$i \cdot 9 \cdot (i \cdot \sqrt{16})$

Step 9

Move $9$ to the left of $i$ .

$9 \cdot i \cdot (i \cdot \sqrt{16})$

Step 10

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

$9 i \cdot (i \cdot \sqrt{4^{2}})$

Step 11

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

$9 i \cdot (i \cdot 4)$

Step 12

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

$9 i \cdot (4 \cdot i)$

Step 13

Multiply $9 i (4 i)$ .

Multiply $4$ by $9$ .

$36 i i$

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

$36 (i^{1} i)$

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

$36 (i^{1} i^{1})$

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

$36 i^{1 + 1}$

Add $1$ and $1$ .

$36 i^{2}$

Step 14

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

$36 \cdot - 1$

Step 15

Multiply $36$ by $- 1$ .

$- 36$

Evaluate square root of -81* square root of -16

Related Questions

Support LCMGCF.com by disabling your adblocker.