Evaluate 2 square root of 50-3 square root of 125+ square root of 98

$2 \sqrt{50} - 3 \sqrt{125} + \sqrt{98}$

Step 1

Simplify each term.

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$2 \sqrt{25 (2)} - 3 \sqrt{125} + \sqrt{98}$

Rewrite $25$ as $5^{2}$ .

$2 \sqrt{5^{2} \cdot 2} - 3 \sqrt{125} + \sqrt{98}$

Pull terms out from under the radical.

$2 (5 \sqrt{2}) - 3 \sqrt{125} + \sqrt{98}$

Multiply $5$ by $2$ .

$10 \sqrt{2} - 3 \sqrt{125} + \sqrt{98}$

Rewrite $125$ as $5^{2} \cdot 5$ .

Factor $25$ out of $125$ .

$10 \sqrt{2} - 3 \sqrt{25 (5)} + \sqrt{98}$

Rewrite $25$ as $5^{2}$ .

$10 \sqrt{2} - 3 \sqrt{5^{2} \cdot 5} + \sqrt{98}$

Pull terms out from under the radical.

$10 \sqrt{2} - 3 (5 \sqrt{5}) + \sqrt{98}$

Multiply $5$ by $- 3$ .

$10 \sqrt{2} - 15 \sqrt{5} + \sqrt{98}$

Rewrite $98$ as $7^{2} \cdot 2$ .

Factor $49$ out of $98$ .

$10 \sqrt{2} - 15 \sqrt{5} + \sqrt{49 (2)}$

Rewrite $49$ as $7^{2}$ .

$10 \sqrt{2} - 15 \sqrt{5} + \sqrt{7^{2} \cdot 2}$

Pull terms out from under the radical.

$10 \sqrt{2} - 15 \sqrt{5} + 7 \sqrt{2}$

Step 2

Add $10 \sqrt{2}$ and $7 \sqrt{2}$ .

$17 \sqrt{2} - 15 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$17 \sqrt{2} - 15 \sqrt{5}$

Decimal Form:

$- 9.49938910 \dots$