Solve sqrt{25/36/frac{10{16}}}

$$\sqrt { \frac { \frac { 25 } { 36 } } { \frac { 10 } { 16 } } }$$

Evaluate

$$\frac{\sqrt{10}}{3}\approx 1.054092553$$

Solution Steps

Divide \frac{25}{36} by \frac{10}{16} by multiplying \frac{25}{36} by the reciprocal of \frac{10}{16}.

$$\sqrt{\frac{25\times 16}{36\times 10}}$$

Cancel out 2\times 4\times 5 in both numerator and denominator.

$$\sqrt{\frac{2\times 5}{9}}$$

Multiply 2 and 5 to get 10.

$$\sqrt{\frac{10}{9}}$$

Rewrite the square root of the division \sqrt{\frac{10}{9}} as the division of square roots \frac{\sqrt{10}}{\sqrt{9}}.

$$\frac{\sqrt{10}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{\sqrt{10}}{3}$$