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

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

Evaluate

$$\frac{4\sqrt{65}}{65}\approx 0.496138938$$

Solution Steps

Calculate \frac{4}{3} to the power of 2 and get \frac{16}{9}.

$$\frac{\frac{4}{3}}{\sqrt{9-\frac{16}{9}}}$$

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

$$\frac{\frac{4}{3}}{\sqrt{\frac{81}{9}-\frac{16}{9}}}$$

Since \frac{81}{9} and \frac{16}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4}{3}}{\sqrt{\frac{81-16}{9}}}$$

Subtract 16 from 81 to get 65.

$$\frac{\frac{4}{3}}{\sqrt{\frac{65}{9}}}$$

Rewrite the square root of the division \sqrt{\frac{65}{9}} as the division of square roots \frac{\sqrt{65}}{\sqrt{9}}.

$$\frac{\frac{4}{3}}{\frac{\sqrt{65}}{\sqrt{9}}}$$

Calculate the square root of 9 and get 3.

$$\frac{\frac{4}{3}}{\frac{\sqrt{65}}{3}}$$

Divide \frac{4}{3} by \frac{\sqrt{65}}{3} by multiplying \frac{4}{3} by the reciprocal of \frac{\sqrt{65}}{3}.

$$\frac{4\times 3}{3\sqrt{65}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{4}{\sqrt{65}}$$

Rationalize the denominator of \frac{4}{\sqrt{65}} by multiplying numerator and denominator by \sqrt{65}.

$$\frac{4\sqrt{65}}{\left(\sqrt{65}\right)^{2}}$$

The square of \sqrt{65} is 65.

$$\frac{4\sqrt{65}}{65}$$