Pre-Algebra Examples

$\sqrt{5} - 3 i + (- 2 + \sqrt{- 9})$

Step 1

Remove parentheses.

$\sqrt{5} - 3 i - 2 + \sqrt{- 9}$

Step 2

Simplify each term.

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Step 2.1

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

$\sqrt{5} - 3 i - 2 + \sqrt{- 1 (9)}$

Step 2.2

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

$\sqrt{5} - 3 i - 2 + \sqrt{- 1} \cdot \sqrt{9}$

Step 2.3

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

$\sqrt{5} - 3 i - 2 + i \cdot \sqrt{9}$

Step 2.4

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

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

Step 2.5

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

$\sqrt{5} - 3 i - 2 + i \cdot 3$

Step 2.6

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

$\sqrt{5} - 3 i - 2 + 3 i$

Step 3

Simplify by adding terms.

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Step 3.1

Add $- 3 i$ and $3 i$ .

$\sqrt{5} + 0 - 2$

Step 3.2

Add $\sqrt{5}$ and $0$ .

$\sqrt{5} - 2$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{5} - 2$

Decimal Form:

$0.23606797 \dots$