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

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

Evaluate

$$-\frac{23}{4}=-5.75$$

Solution Steps

Least common multiple of 4 and 8 is 8. Convert \frac{7}{4} and \frac{5}{8} to fractions with denominator 8.

$$-7+\sqrt{\frac{14}{8}-\frac{5}{8}+\frac{7}{16}}$$

Since \frac{14}{8} and \frac{5}{8} have the same denominator, subtract them by subtracting their numerators.

$$-7+\sqrt{\frac{14-5}{8}+\frac{7}{16}}$$

Subtract 5 from 14 to get 9.

$$-7+\sqrt{\frac{9}{8}+\frac{7}{16}}$$

Least common multiple of 8 and 16 is 16. Convert \frac{9}{8} and \frac{7}{16} to fractions with denominator 16.

$$-7+\sqrt{\frac{18}{16}+\frac{7}{16}}$$

Since \frac{18}{16} and \frac{7}{16} have the same denominator, add them by adding their numerators.

$$-7+\sqrt{\frac{18+7}{16}}$$

Add 18 and 7 to get 25.

$$-7+\sqrt{\frac{25}{16}}$$

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.

$$-7+\frac{5}{4}$$

Convert -7 to fraction -\frac{28}{4}.

$$-\frac{28}{4}+\frac{5}{4}$$

Since -\frac{28}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$\frac{-28+5}{4}$$

Add -28 and 5 to get -23.

$$-\frac{23}{4}$$

Factor

$$-\frac{23}{4} = -5\frac{3}{4} = -5.75$$