Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $9$ out of $18$ .

$\sqrt{9 (2)} + \sqrt{32}$

Step 1.1.2

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

$\sqrt{3^{2} \cdot 2} + \sqrt{32}$

$\sqrt{3^{2} \cdot 2} + \sqrt{32}$

Step 1.2

Pull terms out from under the radical.

$3 \sqrt{2} + \sqrt{32}$

Step 1.3

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

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Step 1.3.1

Factor $16$ out of $32$ .

$3 \sqrt{2} + \sqrt{16 (2)}$

Step 1.3.2

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

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

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

Step 1.4

Pull terms out from under the radical.

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

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

Step 2

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

$7 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt{2}$

Decimal Form:

$9.89949493 \dots$

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