Solve sqrt{3/2}-1/10

$$\sqrt { \frac { 3 } { 2 } } - \frac { 1 } { 10 }$$

Evaluate

$$\frac{\sqrt{6}}{2}-\frac{1}{10}\approx 1.124744871$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{3}{2}} as the division of square roots \frac{\sqrt{3}}{\sqrt{2}}.

$$\frac{\sqrt{3}}{\sqrt{2}}-\frac{1}{10}$$

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\frac{1}{10}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{3}\sqrt{2}}{2}-\frac{1}{10}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{6}}{2}-\frac{1}{10}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 10 is 10. Multiply \frac{\sqrt{6}}{2} times \frac{5}{5}.

$$\frac{5\sqrt{6}}{10}-\frac{1}{10}$$

Since \frac{5\sqrt{6}}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\sqrt{6}-1}{10}$$

Factor

$$\frac{5 \sqrt{6} - 1}{10} = 1.124744871391589$$