Solve -{[(1/sqrt{4})-(-1/sqrt{9})]+(-sqrt{4})^3+2(sqrt{16}-1/2)}div(3/4)

$$- \{ [ ( \frac { 1 } { \sqrt { 4 } } ) - ( - \frac { 1 } { \sqrt { 9 } } ) ] + ( - \sqrt { 4 } ) ^ { 3 } + 2 ( \sqrt { 16 } - \frac { 1 } { 2 } ) \} \div ( \frac { 3 } { 4 } )$$

Evaluate

$$\frac{2}{9}\approx 0.222222222$$

Solution Steps

Calculate the square root of 4 and get 2.

$$\frac{-\left(\frac{1}{2}-\left(-\frac{1}{\sqrt{9}}\right)+\left(-\sqrt{4}\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Calculate the square root of 9 and get 3.

$$\frac{-\left(\frac{1}{2}-\left(-\frac{1}{3}\right)+\left(-\sqrt{4}\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

The opposite of -\frac{1}{3} is \frac{1}{3}.

$$\frac{-\left(\frac{1}{2}+\frac{1}{3}+\left(-\sqrt{4}\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Add \frac{1}{2} and \frac{1}{3} to get \frac{5}{6}.

$$\frac{-\left(\frac{5}{6}+\left(-\sqrt{4}\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{-\left(\frac{5}{6}+\left(-2\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{-\left(\frac{5}{6}-8+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Subtract 8 from \frac{5}{6} to get -\frac{43}{6}.

$$\frac{-\left(-\frac{43}{6}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Calculate the square root of 16 and get 4.

$$\frac{-\left(-\frac{43}{6}+2\left(4-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

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

$$\frac{-\left(-\frac{43}{6}+2\times \frac{7}{2}\right)}{\frac{3}{4}}$$

Multiply 2 and \frac{7}{2} to get 7.

$$\frac{-\left(-\frac{43}{6}+7\right)}{\frac{3}{4}}$$

Add -\frac{43}{6} and 7 to get -\frac{1}{6}.

$$\frac{-\left(-\frac{1}{6}\right)}{\frac{3}{4}}$$

The opposite of -\frac{1}{6} is \frac{1}{6}.

$$\frac{\frac{1}{6}}{\frac{3}{4}}$$

Divide \frac{1}{6} by \frac{3}{4} by multiplying \frac{1}{6} by the reciprocal of \frac{3}{4}.

$$\frac{1}{6}\times \frac{4}{3}$$

Multiply \frac{1}{6} and \frac{4}{3} to get \frac{2}{9}.

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

Factor

$$\frac{2}{3 ^ {2}} = 0.2222222222222222$$