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Evaluate 5 square root of 2+ square root of 18

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

Step 1

Simplify each term.

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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