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

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

Evaluate

$$-\frac{8}{3}\approx -2.666666667$$

Solution Steps

Subtract \frac{1}{9} from 1 to get \frac{8}{9}.

$$\sqrt[3]{\frac{8}{9}\left(\frac{2}{3}-1\right)}-\sqrt{\left(-4\right)^{2}}\sqrt{\frac{1}{4}}$$

Subtract 1 from \frac{2}{3} to get -\frac{1}{3}.

$$\sqrt[3]{\frac{8}{9}\left(-\frac{1}{3}\right)}-\sqrt{\left(-4\right)^{2}}\sqrt{\frac{1}{4}}$$

Multiply \frac{8}{9} and -\frac{1}{3} to get -\frac{8}{27}.

$$\sqrt[3]{-\frac{8}{27}}-\sqrt{\left(-4\right)^{2}}\sqrt{\frac{1}{4}}$$

Calculate \sqrt[3]{-\frac{8}{27}} and get -\frac{2}{3}.

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

Calculate -4 to the power of 2 and get 16.

$$-\frac{2}{3}-\sqrt{16}\sqrt{\frac{1}{4}}$$

Calculate the square root of 16 and get 4.

$$-\frac{2}{3}-4\sqrt{\frac{1}{4}}$$

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.

$$-\frac{2}{3}-4\times \frac{1}{2}$$

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

$$-\frac{2}{3}-2$$

Subtract 2 from -\frac{2}{3} to get -\frac{8}{3}.

$$-\frac{8}{3}$$

Factor

$$-\frac{8}{3} = -2\frac{2}{3} = -2.6666666666666665$$