Solve sqrt{7/16+7/4-5/8}

$$\sqrt { \frac { 7 } { 16 } + \frac { 7 } { 4 } - \frac { 5 } { 8 } }$$

Evaluate

$$\frac{5}{4}=1.25$$

Solution Steps

Least common multiple of 16 and 4 is 16. Convert \frac{7}{16} and \frac{7}{4} to fractions with denominator 16.

$$\sqrt{\frac{7}{16}+\frac{28}{16}-\frac{5}{8}}$$

Since \frac{7}{16} and \frac{28}{16} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{7+28}{16}-\frac{5}{8}}$$

Add 7 and 28 to get 35.

$$\sqrt{\frac{35}{16}-\frac{5}{8}}$$

Least common multiple of 16 and 8 is 16. Convert \frac{35}{16} and \frac{5}{8} to fractions with denominator 16.

$$\sqrt{\frac{35}{16}-\frac{10}{16}}$$

Since \frac{35}{16} and \frac{10}{16} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{35-10}{16}}$$

Subtract 10 from 35 to get 25.

$$\sqrt{\frac{25}{16}}$$

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.

$$\frac{5}{4}$$

Factor

$$\frac{5}{2 ^ {2}} = 1\frac{1}{4} = 1.25$$