Solve sqrt{1-(2/3)^2}

$$\sqrt { 1 - ( \frac { 2 } { 3 } ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{5}}{3}\approx 0.745355992$$

Solution Steps

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

$$\sqrt{1-\frac{4}{9}}$$

Convert 1 to fraction \frac{9}{9}.

$$\sqrt{\frac{9}{9}-\frac{4}{9}}$$

Since \frac{9}{9} and \frac{4}{9} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{9-4}{9}}$$

Subtract 4 from 9 to get 5.

$$\sqrt{\frac{5}{9}}$$

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

$$\frac{\sqrt{5}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{\sqrt{5}}{3}$$