Algebra Examples

$i \sqrt{18} + i \sqrt{27}$

Step 1

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

Tap for more steps...

Step 1.1

Factor $9$ out of $18$ .

$i \sqrt{9 (2)} + i \sqrt{27}$

Step 1.2

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

$i \sqrt{3^{2} \cdot 2} + i \sqrt{27}$

$i \sqrt{3^{2} \cdot 2} + i \sqrt{27}$

Step 2

Pull terms out from under the radical.

$i (3 \sqrt{2}) + i \sqrt{27}$

Step 3

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

$3 \cdot i \sqrt{2} + i \sqrt{27}$

Step 4

Rewrite $27$ as $3^{2} \cdot 3$ .

Tap for more steps...

Step 4.1

Factor $9$ out of $27$ .

$3 i \sqrt{2} + i \sqrt{9 (3)}$

Step 4.2

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

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

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

Step 5

Pull terms out from under the radical.

$3 i \sqrt{2} + i (3 \sqrt{3})$

Step 6

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

$3 i \sqrt{2} + 3 i \sqrt{3}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$