Solve sqrt{3/5-1/3}

$$\sqrt { \frac { 3 } { 5 } - \frac { 1 } { 3 } }$$

Evaluate

$$\frac{2\sqrt{15}}{15}\approx 0.516397779$$

Solution Steps

Least common multiple of 5 and 3 is 15. Convert \frac{3}{5} and \frac{1}{3} to fractions with denominator 15.

$$\sqrt{\frac{9}{15}-\frac{5}{15}}$$

Since \frac{9}{15} and \frac{5}{15} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{9-5}{15}}$$

Subtract 5 from 9 to get 4.

$$\sqrt{\frac{4}{15}}$$

Rewrite the square root of the division \sqrt{\frac{4}{15}} as the division of square roots \frac{\sqrt{4}}{\sqrt{15}}.

$$\frac{\sqrt{4}}{\sqrt{15}}$$

Calculate the square root of 4 and get 2.

$$\frac{2}{\sqrt{15}}$$

Rationalize the denominator of \frac{2}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{2\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{2\sqrt{15}}{15}$$