Simplify Simplify: square root of 32+ square root of 8

Simplify: $\sqrt{32} + \sqrt{8}$

Simplify each term.

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

Factor $16$ out of $32$ .

$\sqrt{16 (2)} + \sqrt{8}$

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

$\sqrt{4^{2} \cdot 2} + \sqrt{8}$

$\sqrt{4^{2} \cdot 2} + \sqrt{8}$

Pull terms out from under the radical.

$4 \sqrt{2} + \sqrt{8}$

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

Factor $4$ out of $8$ .

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

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

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

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

Pull terms out from under the radical.

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

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

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

$6 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{2}$

Decimal Form:

$8.48528137 \dots$

Related Questions