Solve sqrt{337/100}-(55/100)^2

$$\sqrt { \frac { 337 } { 100 } } - ( \frac { 55 } { 100 } ) ^ { 2 }$$

Evaluate

$$\frac{\sqrt{337}}{10}-\frac{121}{400}\approx 1.533255975$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{337}{100}} as the division of square roots \frac{\sqrt{337}}{\sqrt{100}}.

$$\frac{\sqrt{337}}{\sqrt{100}}-\left(\frac{55}{100}\right)^{2}$$

Calculate the square root of 100 and get 10.

$$\frac{\sqrt{337}}{10}-\left(\frac{55}{100}\right)^{2}$$

Reduce the fraction \frac{55}{100} to lowest terms by extracting and canceling out 5.

$$\frac{\sqrt{337}}{10}-\left(\frac{11}{20}\right)^{2}$$

Calculate \frac{11}{20} to the power of 2 and get \frac{121}{400}.

$$\frac{\sqrt{337}}{10}-\frac{121}{400}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10 and 400 is 400. Multiply \frac{\sqrt{337}}{10} times \frac{40}{40}.

$$\frac{40\sqrt{337}}{400}-\frac{121}{400}$$

Since \frac{40\sqrt{337}}{400} and \frac{121}{400} have the same denominator, subtract them by subtracting their numerators.

$$\frac{40\sqrt{337}-121}{400}$$

Factor

$$\frac{40 \sqrt{337} - 121}{400} = 1.533255975068582$$