Evaluate -3 square root of 2+3 square root of 20-3 square root of 8

$- 3 \sqrt{2} + 3 \sqrt{20} - 3 \sqrt{8}$

Step 1

Simplify each term.

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$- 3 \sqrt{2} + 3 \sqrt{4 (5)} - 3 \sqrt{8}$

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

$- 3 \sqrt{2} + 3 \sqrt{2^{2} \cdot 5} - 3 \sqrt{8}$

Pull terms out from under the radical.

$- 3 \sqrt{2} + 3 (2 \sqrt{5}) - 3 \sqrt{8}$

Multiply $2$ by $3$ .

$- 3 \sqrt{2} + 6 \sqrt{5} - 3 \sqrt{8}$

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

Factor $4$ out of $8$ .

$- 3 \sqrt{2} + 6 \sqrt{5} - 3 \sqrt{4 (2)}$

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

$- 3 \sqrt{2} + 6 \sqrt{5} - 3 \sqrt{2^{2} \cdot 2}$

Pull terms out from under the radical.

$- 3 \sqrt{2} + 6 \sqrt{5} - 3 (2 \sqrt{2})$

Multiply $2$ by $- 3$ .

$- 3 \sqrt{2} + 6 \sqrt{5} - 6 \sqrt{2}$

Step 2

Subtract $6 \sqrt{2}$ from $- 3 \sqrt{2}$ .

$- 9 \sqrt{2} + 6 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 9 \sqrt{2} + 6 \sqrt{5}$

Decimal Form:

$0.68848580 \dots$