Simplify (-9- square root of 24)/(2(2))

$\frac{- 9 - \sqrt{24}}{2 (2)}$

Simplify the numerator.

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

$\frac{- 9 - \sqrt{4 (6)}}{2 (2)}$

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 1$ .

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

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

Simplify with factoring out.

Multiply $2$ by $2$ .

$\frac{- 9 - 2 \sqrt{6}}{4}$

Rewrite $- 9$ as $- 1 (9)$ .

$\frac{- 1 (9) - 2 \sqrt{6}}{4}$

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

$\frac{- 1 (9) - (2 \sqrt{6})}{4}$

Factor $- 1$ out of $- 1 (9) - (2 \sqrt{6})$ .

$\frac{- 1 (9 + 2 \sqrt{6})}{4}$

Move the negative in front of the fraction.

$- \frac{9 + 2 \sqrt{6}}{4}$

$- \frac{9 + 2 \sqrt{6}}{4}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{9 + 2 \sqrt{6}}{4}$

Decimal Form:

$- 3.47474487 \dots$

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