Solve 0.6-sqrt{19/16}+sqrt{1/100}

$$0.6 - \sqrt { 1 \frac { 9 } { 16 } } + \sqrt { \frac { 1 } { 100 } }$$

Evaluate

$$-0.55$$

Solution Steps

Multiply 1 and 16 to get 16.

$$0.6-\sqrt{\frac{16+9}{16}}+\sqrt{\frac{1}{100}}$$

Add 16 and 9 to get 25.

$$0.6-\sqrt{\frac{25}{16}}+\sqrt{\frac{1}{100}}$$

Rewrite the square root of the division \frac{25}{16} as the division of square roots \frac{\sqrt{25}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$0.6-\frac{5}{4}+\sqrt{\frac{1}{100}}$$

Convert decimal number 0.6 to fraction \frac{6}{10}. Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$\frac{3}{5}-\frac{5}{4}+\sqrt{\frac{1}{100}}$$

Least common multiple of 5 and 4 is 20. Convert \frac{3}{5} and \frac{5}{4} to fractions with denominator 20.

$$\frac{12}{20}-\frac{25}{20}+\sqrt{\frac{1}{100}}$$

Since \frac{12}{20} and \frac{25}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12-25}{20}+\sqrt{\frac{1}{100}}$$

Subtract 25 from 12 to get -13.

$$-\frac{13}{20}+\sqrt{\frac{1}{100}}$$

Rewrite the square root of the division \frac{1}{100} as the division of square roots \frac{\sqrt{1}}{\sqrt{100}}. Take the square root of both numerator and denominator.

$$-\frac{13}{20}+\frac{1}{10}$$

Least common multiple of 20 and 10 is 20. Convert -\frac{13}{20} and \frac{1}{10} to fractions with denominator 20.

$$-\frac{13}{20}+\frac{2}{20}$$

Since -\frac{13}{20} and \frac{2}{20} have the same denominator, add them by adding their numerators.

$$\frac{-13+2}{20}$$

Add -13 and 2 to get -11.

$$-\frac{11}{20}$$

Factor

$$-0.55$$