Solve sqrt[3]{8}+sqrt{(-2)^2}-sqrt{1/4}+(-1)^2016

$$\sqrt[ 3 ] { 8 } + \sqrt { ( - 2 ) ^ { 2 } } - \sqrt { \frac { 1 } { 4 } } + ( - 1 ) ^ { 2016 }$$

Evaluate

$$\frac{9}{2}=4.5$$

Solution Steps

Calculate \sqrt[3]{8} and get 2.

$$2+\sqrt{\left(-2\right)^{2}}-\sqrt{\frac{1}{4}}+\left(-1\right)^{2016}$$

Calculate -2 to the power of 2 and get 4.

$$2+\sqrt{4}-\sqrt{\frac{1}{4}}+\left(-1\right)^{2016}$$

Calculate the square root of 4 and get 2.

$$2+2-\sqrt{\frac{1}{4}}+\left(-1\right)^{2016}$$

Add 2 and 2 to get 4.

$$4-\sqrt{\frac{1}{4}}+\left(-1\right)^{2016}$$

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$4-\frac{1}{2}+\left(-1\right)^{2016}$$

Subtract \frac{1}{2} from 4 to get \frac{7}{2}.

$$\frac{7}{2}+\left(-1\right)^{2016}$$

Calculate -1 to the power of 2016 and get 1.

$$\frac{7}{2}+1$$

Add \frac{7}{2} and 1 to get \frac{9}{2}.

$$\frac{9}{2}$$

Factor

$$\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5$$