Simplify square root of 2+ square root of 8+ square root of 50

$\sqrt{2} + \sqrt{8} + \sqrt{50}$

Step 1

Simplify each term.

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$\sqrt{2} + \sqrt{4 (2)} + \sqrt{50}$

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

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

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

Pull terms out from under the radical.

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

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

Factor $25$ out of $50$ .

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

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

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

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

Pull terms out from under the radical.

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

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

Step 2

Simplify by adding terms.

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

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

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

$8 \sqrt{2}$

$8 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$8 \sqrt{2}$

Decimal Form:

$11.31370849 \dots$

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