Finite Math Examples

$\sqrt{- 324} - \sqrt{169}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $- 324$ as $- 1 (324)$ .

$\sqrt{- 1 (324)} - \sqrt{169}$

Step 1.2

Rewrite $\sqrt{- 1 (324)}$ as $\sqrt{- 1} \cdot \sqrt{324}$ .

$\sqrt{- 1} \cdot \sqrt{324} - \sqrt{169}$

Step 1.3

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

$i \cdot \sqrt{324} - \sqrt{169}$

Step 1.4

Rewrite $324$ as $18^{2}$ .

$i \cdot \sqrt{18^{2}} - \sqrt{169}$

Step 1.5

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

$i \cdot 18 - \sqrt{169}$

Step 1.6

Move $18$ to the left of $i$ .

$18 \cdot i - \sqrt{169}$

Step 1.7

Rewrite $169$ as $13^{2}$ .

$18 i - \sqrt{13^{2}}$

Step 1.8

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

$18 i - 1 \cdot 13$

Step 1.9

Multiply $- 1$ by $13$ .

$18 i - 13$

Step 2

Reorder $18 i$ and $- 13$ .

$- 13 + 18 i$