Basic Math Examples

$6 - \sqrt{- 90}$

Step 1

Rewrite $- 90$ as $- 1 (90)$ .

$6 - \sqrt{- 1 (90)}$

Step 2

Rewrite $\sqrt{- 1 (90)}$ as $\sqrt{- 1} \cdot \sqrt{90}$ .

$6 - (\sqrt{- 1} \cdot \sqrt{90})$

Step 3

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

$6 - (i \cdot \sqrt{90})$

Step 4

Rewrite $90$ as $3^{2} \cdot 10$ .

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Step 4.1

Factor $9$ out of $90$ .

$6 - (i \cdot \sqrt{9 (10)})$

Step 4.2

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

$6 - (i \cdot \sqrt{3^{2} \cdot 10})$

Step 5

Pull terms out from under the radical.

$6 - (i \cdot (3 \sqrt{10}))$

Step 6

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

$6 - (3 \cdot i \sqrt{10})$

Step 7

Multiply $3$ by $- 1$ .

$6 - 3 i \sqrt{10}$