Solve sqrt{1/16+1/9+1/6}

$$\sqrt { \frac { 1 } { 16 } + \frac { 1 } { 9 } + \frac { 1 } { 6 } }$$

Evaluate

$$\frac{7}{12}\approx 0.583333333$$

Solution Steps

Least common multiple of 16 and 9 is 144. Convert \frac{1}{16} and \frac{1}{9} to fractions with denominator 144.

$$\sqrt{\frac{9}{144}+\frac{16}{144}+\frac{1}{6}}$$

Since \frac{9}{144} and \frac{16}{144} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{9+16}{144}+\frac{1}{6}}$$

Add 9 and 16 to get 25.

$$\sqrt{\frac{25}{144}+\frac{1}{6}}$$

Least common multiple of 144 and 6 is 144. Convert \frac{25}{144} and \frac{1}{6} to fractions with denominator 144.

$$\sqrt{\frac{25}{144}+\frac{24}{144}}$$

Since \frac{25}{144} and \frac{24}{144} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{25+24}{144}}$$

Add 25 and 24 to get 49.

$$\sqrt{\frac{49}{144}}$$

Rewrite the square root of the division \frac{49}{144} as the division of square roots \frac{\sqrt{49}}{\sqrt{144}}. Take the square root of both numerator and denominator.

$$\frac{7}{12}$$

Factor

$$\frac{7}{2 ^ {2} \cdot 3} = 0.5833333333333334$$