Evaluate 2 square root of 90-3 square root of 20+ square root of 40

$2 \sqrt{90} - 3 \sqrt{20} + \sqrt{40}$

Step 1

Simplify each term.

Rewrite $90$ as $3^{2} \cdot 10$ .

Factor $9$ out of $90$ .

$2 \sqrt{9 (10)} - 3 \sqrt{20} + \sqrt{40}$

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

$2 \sqrt{3^{2} \cdot 10} - 3 \sqrt{20} + \sqrt{40}$

Pull terms out from under the radical.

$2 (3 \sqrt{10}) - 3 \sqrt{20} + \sqrt{40}$

Multiply $3$ by $2$ .

$6 \sqrt{10} - 3 \sqrt{20} + \sqrt{40}$

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

Factor $4$ out of $20$ .

$6 \sqrt{10} - 3 \sqrt{4 (5)} + \sqrt{40}$

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

$6 \sqrt{10} - 3 \sqrt{2^{2} \cdot 5} + \sqrt{40}$

Pull terms out from under the radical.

$6 \sqrt{10} - 3 (2 \sqrt{5}) + \sqrt{40}$

Multiply $2$ by $- 3$ .

$6 \sqrt{10} - 6 \sqrt{5} + \sqrt{40}$

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

$6 \sqrt{10} - 6 \sqrt{5} + \sqrt{4 (10)}$

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

$6 \sqrt{10} - 6 \sqrt{5} + \sqrt{2^{2} \cdot 10}$

Pull terms out from under the radical.

$6 \sqrt{10} - 6 \sqrt{5} + 2 \sqrt{10}$

Step 2

Add $6 \sqrt{10}$ and $2 \sqrt{10}$ .

$8 \sqrt{10} - 6 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$8 \sqrt{10} - 6 \sqrt{5}$

Decimal Form:

$11.88181341 \dots$