Simplify square root of 128-3 square root of 80+2 square root of 450

$\sqrt{128} - 3 \sqrt{80} + 2 \sqrt{450}$

Step 1

Simplify each term.

Rewrite $128$ as $8^{2} \cdot 2$ .

Factor $64$ out of $128$ .

$\sqrt{64 (2)} - 3 \sqrt{80} + 2 \sqrt{450}$

Rewrite $64$ as $8^{2}$ .

$\sqrt{8^{2} \cdot 2} - 3 \sqrt{80} + 2 \sqrt{450}$

Pull terms out from under the radical.

$8 \sqrt{2} - 3 \sqrt{80} + 2 \sqrt{450}$

Rewrite $80$ as $4^{2} \cdot 5$ .

Factor $16$ out of $80$ .

$8 \sqrt{2} - 3 \sqrt{16 (5)} + 2 \sqrt{450}$

Rewrite $16$ as $4^{2}$ .

$8 \sqrt{2} - 3 \sqrt{4^{2} \cdot 5} + 2 \sqrt{450}$

Pull terms out from under the radical.

$8 \sqrt{2} - 3 (4 \sqrt{5}) + 2 \sqrt{450}$

Multiply $4$ by $- 3$ .

$8 \sqrt{2} - 12 \sqrt{5} + 2 \sqrt{450}$

Rewrite $450$ as $15^{2} \cdot 2$ .

Factor $225$ out of $450$ .

$8 \sqrt{2} - 12 \sqrt{5} + 2 \sqrt{225 (2)}$

Rewrite $225$ as $15^{2}$ .

$8 \sqrt{2} - 12 \sqrt{5} + 2 \sqrt{15^{2} \cdot 2}$

Pull terms out from under the radical.

$8 \sqrt{2} - 12 \sqrt{5} + 2 (15 \sqrt{2})$

Multiply $15$ by $2$ .

$8 \sqrt{2} - 12 \sqrt{5} + 30 \sqrt{2}$

Step 2

Add $8 \sqrt{2}$ and $30 \sqrt{2}$ .

$38 \sqrt{2} - 12 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$38 \sqrt{2} - 12 \sqrt{5}$

Decimal Form:

$26.90729964 \dots$