Simplify square root of -15* square root of -4

$\sqrt{- 15} \cdot \sqrt{- 4}$

Step 1

Rewrite $- 15$ as $- 1 (15)$ .

$\sqrt{- 1 (15)} \cdot \sqrt{- 4}$

Step 2

Rewrite $\sqrt{- 1 (15)}$ as $\sqrt{- 1} \cdot \sqrt{15}$ .

$\sqrt{- 1} \cdot \sqrt{15} \cdot \sqrt{- 4}$

Step 3

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

$i \cdot \sqrt{15} \cdot \sqrt{- 4}$

Step 4

Rewrite $- 4$ as $- 1 (4)$ .

$i \cdot \sqrt{15} \cdot \sqrt{- 1 (4)}$

Step 5

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$i \cdot \sqrt{15} \cdot (\sqrt{- 1} \cdot \sqrt{4})$

Step 6

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

$i \cdot \sqrt{15} \cdot (i \cdot \sqrt{4})$

Step 7

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

$i \sqrt{15} \cdot (i \cdot \sqrt{2^{2}})$

Step 8

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

$i \sqrt{15} \cdot (i \cdot 2)$

Step 9

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

$i \sqrt{15} \cdot (2 \cdot i)$

Step 10

Multiply $i \sqrt{15} (2 i)$ .

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

$\sqrt{15} (2 (i^{1} i))$

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

$\sqrt{15} (2 (i^{1} i^{1}))$

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

$\sqrt{15} (2 i^{1 + 1})$

Add $1$ and $1$ .

$\sqrt{15} (2 i^{2})$

Step 11

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

$\sqrt{15} (2 \cdot - 1)$

Step 12

Multiply $2$ by $- 1$ .

$\sqrt{15} \cdot - 2$

Step 13

Move $- 2$ to the left of $\sqrt{15}$ .

$- 2 \sqrt{15}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$- 2 \sqrt{15}$

Decimal Form:

$- 7.74596669 \dots$

Simplify square root of -15* square root of -4

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