Solve sqrt{1/49}-sqrt{4/81}

$$\sqrt { \frac { 1 } { 49 } } - \sqrt { \frac { 4 } { 81 } }$$

Evaluate

$$-\frac{5}{63}\approx -0.079365079$$

Solution Steps

Rewrite the square root of the division \frac{1}{49} as the division of square roots \frac{\sqrt{1}}{\sqrt{49}}. Take the square root of both numerator and denominator.

$$\frac{1}{7}-\sqrt{\frac{4}{81}}$$

Rewrite the square root of the division \frac{4}{81} as the division of square roots \frac{\sqrt{4}}{\sqrt{81}}. Take the square root of both numerator and denominator.

$$\frac{1}{7}-\frac{2}{9}$$

Least common multiple of 7 and 9 is 63. Convert \frac{1}{7} and \frac{2}{9} to fractions with denominator 63.

$$\frac{9}{63}-\frac{14}{63}$$

Since \frac{9}{63} and \frac{14}{63} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-14}{63}$$

Subtract 14 from 9 to get -5.

$$-\frac{5}{63}$$

Factor

$$-\frac{5}{63} = -0.07936507936507936$$