Solve sqrt{81}+sqrt[3]{-27}+sqrt{(-2/3)^2}-1-21

$$\sqrt { 81 } + \sqrt[ 3 ] { - 27 } + \sqrt { ( - \frac { 2 } { 3 } ) ^ { 2 } } - 1 - 21$$

Evaluate

$$-\frac{46}{3}\approx -15.333333333$$

Solution Steps

Calculate the square root of 81 and get 9.

$$9+\sqrt[3]{-27}+\sqrt{\left(-\frac{2}{3}\right)^{2}}-1-21$$

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

$$9-3+\sqrt{\left(-\frac{2}{3}\right)^{2}}-1-21$$

Subtract 3 from 9 to get 6.

$$6+\sqrt{\left(-\frac{2}{3}\right)^{2}}-1-21$$

Calculate -\frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$6+\sqrt{\frac{4}{9}}-1-21$$

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

$$6+\frac{2}{3}-1-21$$

Add 6 and \frac{2}{3} to get \frac{20}{3}.

$$\frac{20}{3}-1-21$$

Subtract 1 from \frac{20}{3} to get \frac{17}{3}.

$$\frac{17}{3}-21$$

Subtract 21 from \frac{17}{3} to get -\frac{46}{3}.

$$-\frac{46}{3}$$

Factor

$$-\frac{46}{3} = -15\frac{1}{3} = -15.333333333333334$$