Simplify (-8+ square root of 64-28)/(2(-3))

$\frac{- 8 + \sqrt{64 - 28}}{2 (- 3)}$

Simplify the numerator.

Subtract $28$ from $64$ .

$\frac{- 8 + \sqrt{36}}{2 (- 3)}$

Rewrite $36$ as $6^{2}$ .

$\frac{- 8 + \sqrt{6^{2}}}{2 (- 3)}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{- 8 + 6}{2 (- 3)}$

Add $- 8$ and $6$ .

$\frac{- 2}{2 (- 3)}$

Reduce the expression by cancelling the common factors.

Multiply $2$ by $- 3$ .

$\frac{- 2}{- 6}$

Cancel the common factor of $- 2$ and $- 6$ .

Factor $- 2$ out of $- 2$ .

$\frac{- 2 (1)}{- 6}$

Cancel the common factors.

Factor $- 2$ out of $- 6$ .

$\frac{- 2 \cdot 1}{- 2 \cdot 3}$

Cancel the common factor.

$\frac{- 2 \cdot 1}{- 2 \cdot 3}$

Rewrite the expression.

$\frac{1}{3}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$