Find the Exact Value square root of 8+ square root of 32- square root of 2

$\sqrt{8} + \sqrt{32} - \sqrt{2}$

Simplify each term.

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

Factor $4$ out of $8$ .

$\sqrt{4 (2)} + \sqrt{32} - \sqrt{2}$

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

$\sqrt{2^{2} \cdot 2} + \sqrt{32} - \sqrt{2}$

$\sqrt{2^{2} \cdot 2} + \sqrt{32} - \sqrt{2}$

Pull terms out from under the radical.

$2 \sqrt{2} + \sqrt{32} - \sqrt{2}$

Rewrite $32$ as $4^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$2 \sqrt{2} + \sqrt{16 (2)} - \sqrt{2}$

Rewrite $16$ as $4^{2}$ .

$2 \sqrt{2} + \sqrt{4^{2} \cdot 2} - \sqrt{2}$

$2 \sqrt{2} + \sqrt{4^{2} \cdot 2} - \sqrt{2}$

Pull terms out from under the radical.

$2 \sqrt{2} + 4 \sqrt{2} - \sqrt{2}$

$2 \sqrt{2} + 4 \sqrt{2} - \sqrt{2}$

Simplify by adding terms.

Add $2 \sqrt{2}$ and $4 \sqrt{2}$ .

$6 \sqrt{2} - \sqrt{2}$

Subtract $\sqrt{2}$ from $6 \sqrt{2}$ .

$5 \sqrt{2}$

$5 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{2}$

Decimal Form:

$7.07106781 \dots$

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