Simplify ( square root of -2)( square root of -24)

$(\sqrt{- 2}) (\sqrt{- 24})$

Step 1

Rewrite $- 2$ as $- 1 (2)$ .

$\sqrt{- 1 (2)} \sqrt{- 24}$

Step 2

Rewrite $\sqrt{- 1 (2)}$ as $\sqrt{- 1} \cdot \sqrt{2}$ .

$\sqrt{- 1} \cdot \sqrt{2} \sqrt{- 24}$

Step 3

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

$i \cdot \sqrt{2} \sqrt{- 24}$

Step 4

Rewrite $- 24$ as $- 1 (24)$ .

$i \cdot \sqrt{2} \sqrt{- 1 (24)}$

Step 5

Rewrite $\sqrt{- 1 (24)}$ as $\sqrt{- 1} \cdot \sqrt{24}$ .

$i \cdot \sqrt{2} (\sqrt{- 1} \cdot \sqrt{24})$

Step 6

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

$i \cdot \sqrt{2} (i \cdot \sqrt{24})$

Step 7

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

$i \sqrt{2} (i \cdot \sqrt{4 (6)})$

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

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

Step 8

Pull terms out from under the radical.

$i \sqrt{2} (i \cdot (2 \sqrt{6}))$

Step 9

Move $2$ to the left of $i$ .

$i \sqrt{2} (2 \cdot i \sqrt{6})$

Step 10

Multiply $i \sqrt{2} (2 i \sqrt{6})$ .

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

$\sqrt{2} (2 (i^{1} i) \sqrt{6})$

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

$\sqrt{2} (2 (i^{1} i^{1}) \sqrt{6})$

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

$\sqrt{2} (2 i^{1 + 1} \sqrt{6})$

Add $1$ and $1$ .

$\sqrt{2} (2 i^{2} \sqrt{6})$

Combine using the product rule for radicals.

$2 i^{2} \sqrt{2 \cdot 6}$

Multiply $2$ by $6$ .

$2 i^{2} \sqrt{12}$

Step 11

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

$2 \cdot - 1 \sqrt{12}$

Step 12

Multiply $2$ by $- 1$ .

$- 2 \sqrt{12}$

Step 13

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$- 2 \sqrt{4 (3)}$

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

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

Step 14

Pull terms out from under the radical.

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

Step 15

Multiply $2$ by $- 2$ .

$- 4 \sqrt{3}$

Step 16

The result can be shown in multiple forms.

Exact Form:

$- 4 \sqrt{3}$

Decimal Form:

$- 6.92820323 \dots$

Simplify ( square root of -2)( square root of -24)

Related Questions

Support LCMGCF.com by disabling your adblocker.