Simplify i square root of 18+i square root of 27

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

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

Factor $9$ out of $18$ .

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

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

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

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

Pull terms out from under the radical.

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

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

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

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

Factor $9$ out of $27$ .

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

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

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

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

Pull terms out from under the radical.

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

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

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

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