Solve sqrt{100/64}+215/8

$$\sqrt { \frac { 100 } { 64 } } + 2 \frac { 15 } { 8 }$$

Evaluate

$$\frac{41}{8}=5.125$$

Solution Steps

Reduce the fraction \frac{100}{64} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{25}{16}}+\frac{2\times 8+15}{8}$$

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.

$$\frac{5}{4}+\frac{2\times 8+15}{8}$$

Multiply 2 and 8 to get 16.

$$\frac{5}{4}+\frac{16+15}{8}$$

Add 16 and 15 to get 31.

$$\frac{5}{4}+\frac{31}{8}$$

Least common multiple of 4 and 8 is 8. Convert \frac{5}{4} and \frac{31}{8} to fractions with denominator 8.

$$\frac{10}{8}+\frac{31}{8}$$

Since \frac{10}{8} and \frac{31}{8} have the same denominator, add them by adding their numerators.

$$\frac{10+31}{8}$$

Add 10 and 31 to get 41.

$$\frac{41}{8}$$

Factor

$$\frac{41}{2 ^ {3}} = 5\frac{1}{8} = 5.125$$