Solve frac{12+sqrt{96}}{2}-(4+3+5)

$$\frac{ 12+ \sqrt{ 96 } }{ 2 } -(4+3+5)$$

Evaluate

$$2\left(\sqrt{6}-3\right)\approx -1.101020514$$

Short Solution Steps

Factor 96=4^{2}\times 6. Rewrite the square root of the product \sqrt{4^{2}\times 6} as the product of square roots \sqrt{4^{2}}\sqrt{6}. Take the square root of 4^{2}.

$$\frac{12+4\sqrt{6}}{2}-\left(4+3+5\right)$$

Add 4 and 3 to get 7.

$$\frac{12+4\sqrt{6}}{2}-\left(7+5\right)$$

Add 7 and 5 to get 12.

$$\frac{12+4\sqrt{6}}{2}-12$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 12 times \frac{2}{2}.

$$\frac{12+4\sqrt{6}}{2}-\frac{12\times 2}{2}$$

Since \frac{12+4\sqrt{6}}{2} and \frac{12\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12+4\sqrt{6}-12\times 2}{2}$$

Do the multiplications in 12+4\sqrt{6}-12\times 2.

$$\frac{12+4\sqrt{6}-24}{2}$$

Do the calculations in 12+4\sqrt{6}-24.

$$\frac{-12+4\sqrt{6}}{2}$$

Factor

$$2 {(\sqrt{6} - 3)} = -1.101020514$$