Basic Math Examples

$\sqrt{- 18} \cdot \sqrt{- 14}$

Step 1

Rewrite $- 18$ as $- 1 (18)$ .

$\sqrt{- 1 (18)} \cdot \sqrt{- 14}$

Step 2

Rewrite $\sqrt{- 1 (18)}$ as $\sqrt{- 1} \cdot \sqrt{18}$ .

$\sqrt{- 1} \cdot \sqrt{18} \cdot \sqrt{- 14}$

Step 3

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

$i \cdot \sqrt{18} \cdot \sqrt{- 14}$

Step 4

Rewrite $- 14$ as $- 1 (14)$ .

$i \cdot \sqrt{18} \cdot \sqrt{- 1 (14)}$

Step 5

Rewrite $\sqrt{- 1 (14)}$ as $\sqrt{- 1} \cdot \sqrt{14}$ .

$i \cdot \sqrt{18} \cdot (\sqrt{- 1} \cdot \sqrt{14})$

Step 6

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

$i \cdot \sqrt{18} \cdot (i \cdot \sqrt{14})$

Step 7

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 7.1

Factor $9$ out of $18$ .

$i \cdot \sqrt{9 (2)} \cdot (i \cdot \sqrt{14})$

Step 7.2

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

$i \cdot \sqrt{3^{2} \cdot 2} \cdot (i \cdot \sqrt{14})$

Step 8

Pull terms out from under the radical.

$i \cdot (3 \sqrt{2}) \cdot (i \cdot \sqrt{14})$

Step 9

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

$3 \cdot i \sqrt{2} \cdot (i \cdot \sqrt{14})$

Step 10

Multiply $3 i \sqrt{2} (i \sqrt{14})$ .

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Step 10.1

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

$3 (i^{1} i) \sqrt{2} \sqrt{14}$

Step 10.2

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

$3 (i^{1} i^{1}) \sqrt{2} \sqrt{14}$

Step 10.3

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

$3 i^{1 + 1} \sqrt{2} \sqrt{14}$

Step 10.4

Add $1$ and $1$ .

$3 i^{2} \sqrt{2} \sqrt{14}$

Step 10.5

Combine using the product rule for radicals.

$3 i^{2} \sqrt{14 \cdot 2}$

Step 10.6

Multiply $14$ by $2$ .

$3 i^{2} \sqrt{28}$

Step 11

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

$3 \cdot - 1 \sqrt{28}$

Step 12

Multiply $3$ by $- 1$ .

$- 3 \sqrt{28}$

Step 13

Rewrite $28$ as $2^{2} \cdot 7$ .

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Step 13.1

Factor $4$ out of $28$ .

$- 3 \sqrt{4 (7)}$

Step 13.2

Rewrite $4$ as $2^{2}$ .

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

Step 14

Pull terms out from under the radical.

$- 3 (2 \sqrt{7})$

Step 15

Multiply $2$ by $- 3$ .

$- 6 \sqrt{7}$

Step 16

The result can be shown in multiple forms.

Exact Form:

$- 6 \sqrt{7}$

Decimal Form:

$- 15.87450786 \dots$