Evaluate square root of 50+ square root of 18

$\sqrt{50} + \sqrt{18}$

Step 1

Simplify each term.

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

Factor $25$ out of $50$ .

$\sqrt{25 (2)} + \sqrt{18}$

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

$\sqrt{5^{2} \cdot 2} + \sqrt{18}$

$\sqrt{5^{2} \cdot 2} + \sqrt{18}$

Pull terms out from under the radical.

$5 \sqrt{2} + \sqrt{18}$

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$5 \sqrt{2} + \sqrt{9 (2)}$

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

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

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

Pull terms out from under the radical.

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

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

Step 2

Add $5 \sqrt{2}$ and $3 \sqrt{2}$ .

$8 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$8 \sqrt{2}$

Decimal Form:

$11.31370849 \dots$

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