Algebra Examples

$\sqrt{- 9 + - 16}$

Step 1

Replace all occurrences of $+$ $-$ with a single $-$ . A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign because $1 \cdot - 1 = - 1$

$\sqrt{- 9 - 16}$

Step 2

Subtract $16$ from $- 9$ .

$\sqrt{- 25}$

Step 3

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

$\sqrt{- 1 (25)}$

Step 4

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

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

Step 5

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

$i \cdot \sqrt{25}$

Step 6

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

$i \cdot \sqrt{5^{2}}$

Step 7

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

$i \cdot 5$

Step 8

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

$5 i$