Write in Standard Form 5 square root of -8+3 square root of -18

$5 \sqrt{- 8} + 3 \sqrt{- 18}$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Simplify each term.

Rewrite $- 8$ as $- 1 (8)$ .

$5 \sqrt{- 1 (8)} + 3 \sqrt{- 18}$

Rewrite $\sqrt{- 1 (8)}$ as $\sqrt{- 1} \cdot \sqrt{8}$ .

$5 (\sqrt{- 1} \cdot \sqrt{8}) + 3 \sqrt{- 18}$

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

$5 (i \cdot \sqrt{8}) + 3 \sqrt{- 18}$

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$5 (i \cdot \sqrt{4 (2)}) + 3 \sqrt{- 18}$

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

$5 (i \cdot \sqrt{2^{2} \cdot 2}) + 3 \sqrt{- 18}$

Pull terms out from under the radical.

$5 (i \cdot (2 \sqrt{2})) + 3 \sqrt{- 18}$

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

$5 (2 \cdot i \sqrt{2}) + 3 \sqrt{- 18}$

Multiply $2$ by $5$ .

$10 (i \sqrt{2}) + 3 \sqrt{- 18}$

Rewrite $- 18$ as $- 1 (18)$ .

$10 i \sqrt{2} + 3 \sqrt{- 1 (18)}$

Rewrite $\sqrt{- 1 (18)}$ as $\sqrt{- 1} \cdot \sqrt{18}$ .

$10 i \sqrt{2} + 3 (\sqrt{- 1} \cdot \sqrt{18})$

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

$10 i \sqrt{2} + 3 (i \cdot \sqrt{18})$

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

Factor $9$ out of $18$ .

$10 i \sqrt{2} + 3 (i \cdot \sqrt{9 (2)})$

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

$10 i \sqrt{2} + 3 (i \cdot \sqrt{3^{2} \cdot 2})$

Pull terms out from under the radical.

$10 i \sqrt{2} + 3 (i \cdot (3 \sqrt{2}))$

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

$10 i \sqrt{2} + 3 (3 \cdot i \sqrt{2})$

Multiply $3$ by $3$ .

$10 i \sqrt{2} + 9 i \sqrt{2}$

Step 3

Add $10 i \sqrt{2}$ and $9 i \sqrt{2}$ .

$19 i \sqrt{2}$