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

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

Evaluate

$$\frac{14}{3}\approx 4.666666667$$

Solution Steps

Calculate the square root of 81 and get 9.

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

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

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

Subtract 3 from 9 to get 6.

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

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

$$6+\sqrt{\frac{4}{9}}-2$$

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.

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

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

$$\frac{20}{3}-2$$

Subtract 2 from \frac{20}{3} to get \frac{14}{3}.

$$\frac{14}{3}$$

Factor

$$\frac{2 \cdot 7}{3} = 4\frac{2}{3} = 4.666666666666667$$