Simplify (-6+ square root of 18)/(2(2))

$\frac{- 6 + \sqrt{18}}{2 (2)}$

Step 1

Simplify the numerator.

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

Factor $9$ out of $18$ .

$\frac{- 6 + \sqrt{9 (2)}}{2 (2)}$

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

$\frac{- 6 + \sqrt{3^{2} \cdot 2}}{2 (2)}$

$\frac{- 6 + \sqrt{3^{2} \cdot 2}}{2 (2)}$

Pull terms out from under the radical.

$\frac{- 6 + 3 \sqrt{2}}{2 (2)}$

$\frac{- 6 + 3 \sqrt{2}}{2 (2)}$

Step 2

Simplify with factoring out.

Multiply $2$ by $2$ .

$\frac{- 6 + 3 \sqrt{2}}{4}$

Rewrite $- 6$ as $- 1 (6)$ .

$\frac{- 1 (6) + 3 \sqrt{2}}{4}$

Factor $- 1$ out of $3 \sqrt{2}$ .

$\frac{- 1 (6) - (- 3 \sqrt{2})}{4}$

Factor $- 1$ out of $- 1 (6) - (- 3 \sqrt{2})$ .

$\frac{- 1 (6 - 3 \sqrt{2})}{4}$

Move the negative in front of the fraction.

$- \frac{6 - 3 \sqrt{2}}{4}$

$- \frac{6 - 3 \sqrt{2}}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{6 - 3 \sqrt{2}}{4}$

Decimal Form:

$- 0.43933982 \dots$

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