Solve 1-1/21+sqrt{(-1/2)^2}+sqrt[3]{-8}+(-sqrt{3})^2

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

Evaluate

$$2$$

Solution Steps

Multiply \frac{1}{2} and 1 to get \frac{1}{2}.

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

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

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

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

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

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.

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

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

$$1+\sqrt[3]{-8}+\left(-\sqrt{3}\right)^{2}$$

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

$$1-2+\left(-\sqrt{3}\right)^{2}$$

Subtract 2 from 1 to get -1.

$$-1+\left(-\sqrt{3}\right)^{2}$$

Calculate -\sqrt{3} to the power of 2 and get \left(\sqrt{3}\right)^{2}.

$$-1+\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$-1+3$$

Add -1 and 3 to get 2.

$$2$$

Factor

$$2$$