Solve sqrt{1/4}-sqrt{1/9}+sqrt{1/16}

$$\sqrt { \frac { 1 } { 4 } } - \sqrt { \frac { 1 } { 9 } } + \sqrt { \frac { 1 } { 16 } }$$

Evaluate

$$\frac{5}{12}\approx 0.416666667$$

Solution Steps

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{1}{2}-\sqrt{\frac{1}{9}}+\sqrt{\frac{1}{16}}$$

Rewrite the square root of the division \frac{1}{9} as the division of square roots \frac{\sqrt{1}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{1}{2}-\frac{1}{3}+\sqrt{\frac{1}{16}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{3}{6}-\frac{2}{6}+\sqrt{\frac{1}{16}}$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-2}{6}+\sqrt{\frac{1}{16}}$$

Subtract 2 from 3 to get 1.

$$\frac{1}{6}+\sqrt{\frac{1}{16}}$$

Rewrite the square root of the division \frac{1}{16} as the division of square roots \frac{\sqrt{1}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{1}{6}+\frac{1}{4}$$

Least common multiple of 6 and 4 is 12. Convert \frac{1}{6} and \frac{1}{4} to fractions with denominator 12.

$$\frac{2}{12}+\frac{3}{12}$$

Since \frac{2}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{2+3}{12}$$

Add 2 and 3 to get 5.

$$\frac{5}{12}$$

Factor

$$\frac{5}{2 ^ {2} \cdot 3} = 0.4166666666666667$$