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

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

Evaluate

$$\frac{20}{3}\approx 6.666666667$$

Solution Steps

Calculate the square root of 81 and get 9.

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

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

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

Subtract 3 from 9 to get 6.

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

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

$$6+\sqrt{\frac{4}{9}}$$

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.

$$6+\frac{2}{3}$$

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

$$\frac{20}{3}$$

Factor

$$\frac{2 ^ {2} \cdot 5}{3} = 6\frac{2}{3} = 6.666666666666667$$