Evaluate square root of 32- square root of 18

$\sqrt{32} - \sqrt{18}$

Step 1

Simplify each term.

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

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 $3^{2} \cdot 2$ .

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.

$4 \sqrt{2} - (3 \sqrt{2})$

Multiply $3$ by $- 1$ .

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

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

Step 2

Subtract $3 \sqrt{2}$ from $4 \sqrt{2}$ .

$\sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2}$

Decimal Form:

$1.41421356 \dots$

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