Simplify 2 square root of 8- square root of 8

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

Step 1

Simplify each term.

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

Factor $4$ out of $8$ .

$2 \sqrt{4 (2)} - \sqrt{8}$

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

$2 \sqrt{2^{2} \cdot 2} - \sqrt{8}$

$2 \sqrt{2^{2} \cdot 2} - \sqrt{8}$

Pull terms out from under the radical.

$2 (2 \sqrt{2}) - \sqrt{8}$

Multiply $2$ by $2$ .

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

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.

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

Multiply $2$ by $- 1$ .

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

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

Step 2

Subtract $2 \sqrt{2}$ from $4 \sqrt{2}$ .

$2 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{2}$

Decimal Form:

$2.82842712 \dots$

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