Simplify i square root of 3*i square root of 6

$i \sqrt{3} \cdot i \sqrt{6}$

Step 1

Multiply $i \sqrt{3} (i \sqrt{6})$ .

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

$i^{1} i \sqrt{3} \sqrt{6}$

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

$i^{1} i^{1} \sqrt{3} \sqrt{6}$

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

$i^{1 + 1} \sqrt{3} \sqrt{6}$

Add $1$ and $1$ .

$i^{2} \sqrt{3} \sqrt{6}$

Combine using the product rule for radicals.

$i^{2} \sqrt{6 \cdot 3}$

Multiply $6$ by $3$ .

$i^{2} \sqrt{18}$

Step 2

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

$- 1 \sqrt{18}$

Step 3

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

Factor $9$ out of $18$ .

$- 1 \sqrt{9 (2)}$

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

$- 1 \sqrt{3^{2} \cdot 2}$

Step 4

Pull terms out from under the radical.

$- 1 (3 \sqrt{2})$

Step 5

Multiply $3$ by $- 1$ .

$- 3 \sqrt{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- 3 \sqrt{2}$

Decimal Form:

$- 4.24264068 \dots$