Basic Math Examples

$\sqrt{- 4} \cdot \sqrt{- 81}$

Step 1

Rewrite

$- 4$ as

$- 1 (4)$ .

$\sqrt{- 1 (4)} \cdot \sqrt{- 81}$

Step 2

Rewrite

$\sqrt{- 1 (4)}$ as

$\sqrt{- 1} \cdot \sqrt{4}$ .

$\sqrt{- 1} \cdot \sqrt{4} \cdot \sqrt{- 81}$

Step 3

Rewrite

$\sqrt{- 1}$ as

$i$ .

$i \cdot \sqrt{4} \cdot \sqrt{- 81}$

Step 4

Rewrite

$- 81$ as

$- 1 (81)$ .

$i \cdot \sqrt{4} \cdot \sqrt{- 1 (81)}$

Step 5

Rewrite

$\sqrt{- 1 (81)}$ as

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

$i \cdot \sqrt{4} \cdot (\sqrt{- 1} \cdot \sqrt{81})$

Step 6

Rewrite

$\sqrt{- 1}$ as

$i$ .

$i \cdot \sqrt{4} \cdot (i \cdot \sqrt{81})$

Step 7

Rewrite

$4$ as

$2^{2}$ .

$i \cdot \sqrt{2^{2}} \cdot (i \cdot \sqrt{81})$

Step 8

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

$i \cdot 2 \cdot (i \cdot \sqrt{81})$

Step 9

Move

$2$ to the left of

$i$ .

$2 \cdot i \cdot (i \cdot \sqrt{81})$

Step 10

Rewrite

$81$ as

$9^{2}$ .

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

Step 11

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

$2 i \cdot (i \cdot 9)$

Step 12

Move

$9$ to the left of

$i$ .

$2 i \cdot (9 \cdot i)$

Step 13

Multiply

$2 i (9 i)$ .

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Step 13.1

Multiply

$9$ by

$2$ .

$18 i i$

Step 13.2

Raise

$i$ to the power of

$1$ .

$18 (i^{1} i)$

Step 13.3

Raise

$i$ to the power of

$1$ .

$18 (i^{1} i^{1})$

Step 13.4

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$18 i^{1 + 1}$

Step 13.5

Add

$1$ and

$1$ .

$18 i^{2}$

Step 14

Rewrite

$i^{2}$ as

$- 1$ .

$18 \cdot - 1$

Step 15

Multiply

$18$ by

$- 1$ .

$- 18$