Algebra Examples

$\sqrt{32} + \sqrt{18}$

Step 1

Simplify each term.

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

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Factor $16$ out of $32$ .

$\sqrt{16 (2)} + \sqrt{18}$

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

$\sqrt{4^{2} \cdot 2} + \sqrt{18}$

$\sqrt{4^{2} \cdot 2} + \sqrt{18}$

Pull terms out from under the radical.

$4 \sqrt{2} + \sqrt{18}$

Rewrite $18$ as $3^{2} \cdot 2$ .

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Factor $9$ out of $18$ .

$4 \sqrt{2} + \sqrt{9 (2)}$

Rewrite $9$ as $3^{2}$ .

$4 \sqrt{2} + \sqrt{3^{2} \cdot 2}$

$4 \sqrt{2} + \sqrt{3^{2} \cdot 2}$

Pull terms out from under the radical.

$4 \sqrt{2} + 3 \sqrt{2}$

$4 \sqrt{2} + 3 \sqrt{2}$

Step 2

Add $4 \sqrt{2}$ and $3 \sqrt{2}$ .

$7 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt{2}$

Decimal Form:

$9.89949493 \dots$

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