Solve [frac{5sqrt{5}}{53}]+[11/105]

$$[ \frac { 5 \sqrt { 5 } } { 53 } ] + [ \frac { 11 } { 105 } ]$$

Evaluate

$$\frac{5\sqrt{5}}{53}+\frac{11}{105}\approx 0.315711714$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 53 and 105 is 5565. Multiply \frac{5\sqrt{5}}{53} times \frac{105}{105}. Multiply \frac{11}{105} times \frac{53}{53}.

$$\frac{105\times 5\sqrt{5}}{5565}+\frac{11\times 53}{5565}$$

Since \frac{105\times 5\sqrt{5}}{5565} and \frac{11\times 53}{5565} have the same denominator, add them by adding their numerators.

$$\frac{105\times 5\sqrt{5}+11\times 53}{5565}$$

Do the multiplications in 105\times 5\sqrt{5}+11\times 53.

$$\frac{525\sqrt{5}+583}{5565}$$

Factor

$$\frac{525 \sqrt{5} + 583}{5565} = 0.31571171395999814$$