Solve sqrt{51/20-1/5}

$$\sqrt{ \frac{ 51 }{ 20 } - \frac{ 1 }{ 5 } }$$

Evaluate

$$\frac{\sqrt{235}}{10}\approx 1.532970972$$

Solution Steps

Least common multiple of 20 and 5 is 20. Convert \frac{51}{20} and \frac{1}{5} to fractions with denominator 20.

$$\sqrt{\frac{51}{20}-\frac{4}{20}}$$

Since \frac{51}{20} and \frac{4}{20} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{51-4}{20}}$$

Subtract 4 from 51 to get 47.

$$\sqrt{\frac{47}{20}}$$

Rewrite the square root of the division \sqrt{\frac{47}{20}} as the division of square roots \frac{\sqrt{47}}{\sqrt{20}}.

$$\frac{\sqrt{47}}{\sqrt{20}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{\sqrt{47}}{2\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{47}}{2\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{47}\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{47}\sqrt{5}}{2\times 5}$$

To multiply \sqrt{47} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{235}}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$\frac{\sqrt{235}}{10}$$