Solve -sqrt[3]{8}divsqrt{21/4}+sqrt{(-1)^100}

$$- \sqrt[ 3 ] { 8 } \div \sqrt { 2 \frac { 1 } { 4 } } + \sqrt { ( - 1 ) ^ { 100 } }$$

Evaluate

$$-\frac{1}{3}\approx -0.333333333$$

Solution Steps

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

$$\frac{-2}{\sqrt{\frac{2\times 4+1}{4}}}+\sqrt{\left(-1\right)^{100}}$$

Multiply 2 and 4 to get 8.

$$\frac{-2}{\sqrt{\frac{8+1}{4}}}+\sqrt{\left(-1\right)^{100}}$$

Add 8 and 1 to get 9.

$$\frac{-2}{\sqrt{\frac{9}{4}}}+\sqrt{\left(-1\right)^{100}}$$

Rewrite the square root of the division \frac{9}{4} as the division of square roots \frac{\sqrt{9}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{-2}{\frac{3}{2}}+\sqrt{\left(-1\right)^{100}}$$

Divide -2 by \frac{3}{2} by multiplying -2 by the reciprocal of \frac{3}{2}.

$$-2\times \frac{2}{3}+\sqrt{\left(-1\right)^{100}}$$

Multiply -2 and \frac{2}{3} to get -\frac{4}{3}.

$$-\frac{4}{3}+\sqrt{\left(-1\right)^{100}}$$

Calculate -1 to the power of 100 and get 1.

$$-\frac{4}{3}+\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$-\frac{4}{3}+1$$

Add -\frac{4}{3} and 1 to get -\frac{1}{3}.

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

Factor

$$-\frac{1}{3} = -0.3333333333333333$$