Algebra Examples

$\sqrt{- 63}$

Step 1

Rewrite $- 63$ as $- 1 (63)$ .

$\sqrt{- 1 (63)}$

Step 2

Rewrite $\sqrt{- 1 (63)}$ as $\sqrt{- 1} \cdot \sqrt{63}$ .

$\sqrt{- 1} \cdot \sqrt{63}$

Step 3

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

$i \cdot \sqrt{63}$

Step 4

Rewrite $63$ as $3^{2} \cdot 7$ .

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Step 4.1

Factor $9$ out of $63$ .

$i \cdot \sqrt{9 (7)}$

Step 4.2

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

$i \cdot \sqrt{3^{2} \cdot 7}$

Step 5

Pull terms out from under the radical.

$i \cdot (3 \sqrt{7})$

Step 6

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

$3 i \sqrt{7}$