Solve sqrt{162/200}-frac{sqrt{55}}{12}

$$\sqrt { \frac { 162 } { 200 } } - \frac { \sqrt { 55 } } { 12 }$$

Evaluate

$$-\frac{\sqrt{55}}{12}+\frac{9}{10}\approx 0.281983459$$

Short Solution Steps

Reduce the fraction \frac{162}{200} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{81}{100}}-\frac{\sqrt{55}}{12}$$

Rewrite the square root of the division \frac{81}{100} as the division of square roots \frac{\sqrt{81}}{\sqrt{100}}. Take the square root of both numerator and denominator.

$$\frac{9}{10}-\frac{\sqrt{55}}{12}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10 and 12 is 60. Multiply \frac{9}{10} times \frac{6}{6}. Multiply \frac{\sqrt{55}}{12} times \frac{5}{5}.

$$\frac{9\times 6}{60}-\frac{5\sqrt{55}}{60}$$

Since \frac{9\times 6}{60} and \frac{5\sqrt{55}}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9\times 6-5\sqrt{55}}{60}$$

Do the multiplications in 9\times 6-5\sqrt{55}.

$$\frac{54-5\sqrt{55}}{60}$$

Factor

$$\frac{54 - 5 \sqrt{55}}{60} = 0.28198345940869474$$