Pre-Algebra Examples

$\sqrt{2}$ , $\sqrt{8}$

Step 1

Add the expressions.

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

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Factor $4$ out of $8$ .

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

Step 2.1.2

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

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

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

Step 2.2

Pull terms out from under the radical.

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

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

Step 3

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

$3 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{2}$

Decimal Form:

$4.24264068 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$