Evaluate square root of -25+ square root of -16+ square root of -9

$\sqrt{- 25} + \sqrt{- 16} + \sqrt{- 9}$

Step 1

Simplify each term.

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

$\sqrt{- 1 (25)} + \sqrt{- 16} + \sqrt{- 9}$

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

$\sqrt{- 1} \cdot \sqrt{25} + \sqrt{- 16} + \sqrt{- 9}$

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

$i \cdot \sqrt{25} + \sqrt{- 16} + \sqrt{- 9}$

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

$i \cdot \sqrt{5^{2}} + \sqrt{- 16} + \sqrt{- 9}$

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

$i \cdot 5 + \sqrt{- 16} + \sqrt{- 9}$

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

$5 \cdot i + \sqrt{- 16} + \sqrt{- 9}$

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

$5 i + \sqrt{- 1 (16)} + \sqrt{- 9}$

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

$5 i + \sqrt{- 1} \cdot \sqrt{16} + \sqrt{- 9}$

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

$5 i + i \cdot \sqrt{16} + \sqrt{- 9}$

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

$5 i + i \cdot \sqrt{4^{2}} + \sqrt{- 9}$

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

$5 i + i \cdot 4 + \sqrt{- 9}$

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

$5 i + 4 \cdot i + \sqrt{- 9}$

Rewrite $- 9$ as $- 1 (9)$ .

$5 i + 4 i + \sqrt{- 1 (9)}$

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$5 i + 4 i + \sqrt{- 1} \cdot \sqrt{9}$

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

$5 i + 4 i + i \cdot \sqrt{9}$

Rewrite $9$ as $3^{2}$ .

$5 i + 4 i + i \cdot \sqrt{3^{2}}$

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

$5 i + 4 i + i \cdot 3$

Move $3$ to the left of $i$ .

$5 i + 4 i + 3 i$

Step 2

Simplify by adding terms.

Add $5 i$ and $4 i$ .

$9 i + 3 i$

Add $9 i$ and $3 i$ .

$12 i$