Basic Math Examples

$\sqrt{- 5} \cdot \sqrt{- 9}$

Step 1

Rewrite $- 5$ as $- 1 (5)$ .

$\sqrt{- 1 (5)} \cdot \sqrt{- 9}$

Step 2

Rewrite $\sqrt{- 1 (5)}$ as $\sqrt{- 1} \cdot \sqrt{5}$ .

$\sqrt{- 1} \cdot \sqrt{5} \cdot \sqrt{- 9}$

Step 3

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

$i \cdot \sqrt{5} \cdot \sqrt{- 9}$

Step 4

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

$i \cdot \sqrt{5} \cdot \sqrt{- 1 (9)}$

Step 5

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

$i \cdot \sqrt{5} \cdot (\sqrt{- 1} \cdot \sqrt{9})$

Step 6

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

$i \cdot \sqrt{5} \cdot (i \cdot \sqrt{9})$

Step 7

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

$i \sqrt{5} \cdot (i \cdot \sqrt{3^{2}})$

Step 8

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

$i \sqrt{5} \cdot (i \cdot 3)$

Step 9

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

$i \sqrt{5} \cdot (3 \cdot i)$

Step 10

Multiply $i \sqrt{5} (3 i)$ .

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Step 10.1

Raise $i$ to the power of $1$ .

$\sqrt{5} (3 (i^{1} i))$

Step 10.2

Raise $i$ to the power of $1$ .

$\sqrt{5} (3 (i^{1} i^{1}))$

Step 10.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt{5} (3 i^{1 + 1})$

Step 10.4

Add $1$ and $1$ .

$\sqrt{5} (3 i^{2})$

Step 11

Rewrite $i^{2}$ as $- 1$ .

$\sqrt{5} (3 \cdot - 1)$

Step 12

Multiply $3$ by $- 1$ .

$\sqrt{5} \cdot - 3$

Step 13

Move $- 3$ to the left of $\sqrt{5}$ .

$- 3 \sqrt{5}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$- 3 \sqrt{5}$

Decimal Form:

$- 6.70820393 \dots$