Solve sqrt{3^2+(2/3)^2}-(4/9)^3

$$\sqrt { 3 ^ { 2 } + ( \frac { 2 } { 3 } ) ^ { 2 } } - ( \frac { 4 } { 9 } ) ^ { 3 }$$

Evaluate

$$\frac{\sqrt{85}}{3}-\frac{64}{729}\approx 2.985389991$$

Short Solution Steps

Calculate 3 to the power of 2 and get 9.

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

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

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

Convert 9 to fraction \frac{81}{9}.

$$\sqrt{\frac{81}{9}+\frac{4}{9}}-\left(\frac{4}{9}\right)^{3}$$

Since \frac{81}{9} and \frac{4}{9} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{81+4}{9}}-\left(\frac{4}{9}\right)^{3}$$

Add 81 and 4 to get 85.

$$\sqrt{\frac{85}{9}}-\left(\frac{4}{9}\right)^{3}$$

Rewrite the square root of the division \sqrt{\frac{85}{9}} as the division of square roots \frac{\sqrt{85}}{\sqrt{9}}.

$$\frac{\sqrt{85}}{\sqrt{9}}-\left(\frac{4}{9}\right)^{3}$$

Calculate the square root of 9 and get 3.

$$\frac{\sqrt{85}}{3}-\left(\frac{4}{9}\right)^{3}$$

Calculate \frac{4}{9} to the power of 3 and get \frac{64}{729}.

$$\frac{\sqrt{85}}{3}-\frac{64}{729}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 729 is 729. Multiply \frac{\sqrt{85}}{3} times \frac{243}{243}.

$$\frac{243\sqrt{85}}{729}-\frac{64}{729}$$

Since \frac{243\sqrt{85}}{729} and \frac{64}{729} have the same denominator, subtract them by subtracting their numerators.

$$\frac{243\sqrt{85}-64}{729}$$

Factor

$$\frac{243 \sqrt{85} - 64}{729} = 2.985389990565393$$