Basic Math Examples

$(\sqrt{- 25}) (\sqrt{- 81})$

Step 1

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

$\sqrt{- 1 (25)} \sqrt{- 81}$

Step 2

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

$\sqrt{- 1} \cdot \sqrt{25} \sqrt{- 81}$

Step 3

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

$i \cdot \sqrt{25} \sqrt{- 81}$

Step 4

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

$i \cdot \sqrt{25} \sqrt{- 1 (81)}$

Step 5

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

$i \cdot \sqrt{25} (\sqrt{- 1} \cdot \sqrt{81})$

Step 6

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

$i \cdot \sqrt{25} (i \cdot \sqrt{81})$

Step 7

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

$i \cdot \sqrt{5^{2}} (i \cdot \sqrt{81})$

Step 8

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

$i \cdot 5 (i \cdot \sqrt{81})$

Step 9

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

$5 \cdot i (i \cdot \sqrt{81})$

Step 10

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

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

Step 11

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

$5 i (i \cdot 9)$

Step 12

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

$5 i (9 \cdot i)$

Step 13

Multiply $5 i (9 i)$ .

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Step 13.1

Multiply $9$ by $5$ .

$45 i i$

Step 13.2

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

$45 (i^{1} i)$

Step 13.3

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

$45 (i^{1} i^{1})$

Step 13.4

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

$45 i^{1 + 1}$

Step 13.5

Add $1$ and $1$ .

$45 i^{2}$

Step 14

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

$45 \cdot - 1$

Step 15

Multiply $45$ by $- 1$ .

$- 45$