Solve frac{-(-8)+sqrt{64-4*2*5}}{4}

$$\frac { - ( - 8 ) + \sqrt { 64 - 4 \times 2 \times 5 } } { 4 }$$

Evaluate

$$\frac{\sqrt{6}}{2}+2\approx 3.224744871$$

Solution Steps

The opposite of -8 is 8.

$$\frac{8+\sqrt{64-4\times 2\times 5}}{4}$$

Multiply 4 and 2 to get 8.

$$\frac{8+\sqrt{64-8\times 5}}{4}$$

Multiply 8 and 5 to get 40.

$$\frac{8+\sqrt{64-40}}{4}$$

Subtract 40 from 64 to get 24.

$$\frac{8+\sqrt{24}}{4}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\frac{8+2\sqrt{6}}{4}$$