Basic Math Examples

$6 \sqrt{- 9} - 2 \sqrt{- 25}$

Step 1

Simplify each term.

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Step 1.1

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

$6 \sqrt{- 1 (9)} - 2 \sqrt{- 25}$

Step 1.2

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

$6 (\sqrt{- 1} \cdot \sqrt{9}) - 2 \sqrt{- 25}$

Step 1.3

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

$6 (i \cdot \sqrt{9}) - 2 \sqrt{- 25}$

Step 1.4

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

$6 (i \cdot \sqrt{3^{2}}) - 2 \sqrt{- 25}$

Step 1.5

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

$6 (i \cdot 3) - 2 \sqrt{- 25}$

Step 1.6

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

$6 (3 \cdot i) - 2 \sqrt{- 25}$

Step 1.7

Multiply $3$ by $6$ .

$18 i - 2 \sqrt{- 25}$

Step 1.8

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

$18 i - 2 \sqrt{- 1 (25)}$

Step 1.9

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

$18 i - 2 (\sqrt{- 1} \cdot \sqrt{25})$

Step 1.10

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

$18 i - 2 (i \cdot \sqrt{25})$

Step 1.11

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

$18 i - 2 (i \cdot \sqrt{5^{2}})$

Step 1.12

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

$18 i - 2 (i \cdot 5)$

Step 1.13

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

$18 i - 2 (5 \cdot i)$

Step 1.14

Multiply $5$ by $- 2$ .

$18 i - 10 i$

Step 2

Subtract $10 i$ from $18 i$ .

$8 i$