Solve (4/3)/(sqrt{29/9})

$$( \frac { 4 } { 3 } ) / ( \sqrt { \frac { 29 } { 9 } } )$$

Evaluate

$$\frac{4\sqrt{29}}{29}\approx 0.742781353$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{29}{9}} as the division of square roots \frac{\sqrt{29}}{\sqrt{9}}.

$$\frac{\frac{4}{3}}{\frac{\sqrt{29}}{\sqrt{9}}}$$

Calculate the square root of 9 and get 3.

$$\frac{\frac{4}{3}}{\frac{\sqrt{29}}{3}}$$

Divide \frac{4}{3} by \frac{\sqrt{29}}{3} by multiplying \frac{4}{3} by the reciprocal of \frac{\sqrt{29}}{3}.

$$\frac{4\times 3}{3\sqrt{29}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{4}{\sqrt{29}}$$

Rationalize the denominator of \frac{4}{\sqrt{29}} by multiplying numerator and denominator by \sqrt{29}.

$$\frac{4\sqrt{29}}{\left(\sqrt{29}\right)^{2}}$$

The square of \sqrt{29} is 29.

$$\frac{4\sqrt{29}}{29}$$