Simplify 1/2 square root of 18

$\frac{1}{2} \sqrt{18}$

Step 1

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

Factor $9$ out of $18$ .

$\frac{1}{2} \cdot \sqrt{9 (2)}$

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

$\frac{1}{2} \cdot \sqrt{3^{2} \cdot 2}$

$\frac{1}{2} \cdot \sqrt{3^{2} \cdot 2}$

Step 2

Pull terms out from under the radical.

$\frac{1}{2} \cdot (3 \sqrt{2})$

Step 3

Multiply $\frac{1}{2} (3 \sqrt{2})$ .

Combine $3$ and $\frac{1}{2}$ .

$\frac{3}{2} \sqrt{2}$

Combine $\frac{3}{2}$ and $\sqrt{2}$ .

$\frac{3 \sqrt{2}}{2}$

$\frac{3 \sqrt{2}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{3 \sqrt{2}}{2}$

Decimal Form:

$2.12132034 \dots$

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