Trigonometry Examples

$\sqrt{- 64} - \sqrt{- 25}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite $- 64$ as $- 1 (64)$ .

$\sqrt{- 1 (64)} - \sqrt{- 25}$

Step 1.2

Rewrite $\sqrt{- 1 (64)}$ as $\sqrt{- 1} \cdot \sqrt{64}$ .

$\sqrt{- 1} \cdot \sqrt{64} - \sqrt{- 25}$

Step 1.3

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

$i \cdot \sqrt{64} - \sqrt{- 25}$

Step 1.4

Rewrite $64$ as $8^{2}$ .

$i \cdot \sqrt{8^{2}} - \sqrt{- 25}$

Step 1.5

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

$i \cdot 8 - \sqrt{- 25}$

Step 1.6

Move $8$ to the left of $i$ .

$8 \cdot i - \sqrt{- 25}$

Step 1.7

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

$8 i - \sqrt{- 1 (25)}$

Step 1.8

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

$8 i - (\sqrt{- 1} \cdot \sqrt{25})$

Step 1.9

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

$8 i - (i \cdot \sqrt{25})$

Step 1.10

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

$8 i - (i \cdot \sqrt{5^{2}})$

Step 1.11

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

$8 i - (i \cdot 5)$

Step 1.12

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

$8 i - (5 \cdot i)$

Step 1.13

Multiply $5$ by $- 1$ .

$8 i - 5 i$

Step 2

Subtract $5 i$ from $8 i$ .

$3 i$