Simplify square root of 121+ square root of 50

$\sqrt{121} + \sqrt{50}$

Step 1

Rewrite $121$ as $11^{2}$ .

$\sqrt{11^{2}} + \sqrt{50}$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

$11 + \sqrt{50}$

Step 3

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

Factor $25$ out of $50$ .

$11 + \sqrt{25 (2)}$

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

$11 + \sqrt{5^{2} \cdot 2}$

Step 4

Pull terms out from under the radical.

$11 + 5 \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$11 + 5 \sqrt{2}$

Decimal Form:

$18.07106781 \dots$