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

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

Evaluate

$$\frac{\sqrt{5}}{3}-\frac{64}{729}\approx 0.657564497$$

Short Solution Steps

Calculate 3 to the power of -2 and get \frac{1}{9}.

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

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

$$\sqrt{\frac{1}{9}+\frac{4}{9}}-\left(\frac{4}{9}\right)^{3}$$

Add \frac{1}{9} and \frac{4}{9} to get \frac{5}{9}.

$$\sqrt{\frac{5}{9}}-\left(\frac{4}{9}\right)^{3}$$

Rewrite the square root of the division \sqrt{\frac{5}{9}} as the division of square roots \frac{\sqrt{5}}{\sqrt{9}}.

$$\frac{\sqrt{5}}{\sqrt{9}}-\left(\frac{4}{9}\right)^{3}$$

Calculate the square root of 9 and get 3.

$$\frac{\sqrt{5}}{3}-\left(\frac{4}{9}\right)^{3}$$

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

$$\frac{\sqrt{5}}{3}-\frac{64}{729}$$

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{5}}{3} times \frac{243}{243}.

$$\frac{243\sqrt{5}}{729}-\frac{64}{729}$$

Since \frac{243\sqrt{5}}{729} and \frac{64}{729} have the same denominator, subtract them by subtracting their numerators.

$$\frac{243\sqrt{5}-64}{729}$$

Factor

$$\frac{243 \sqrt{5} - 64}{729} = 0.6575644973010273$$