Solve 11/2[4/3-sqrt{25/4}-9/2]

$$\frac { 11 } { 2 } [ \frac { 4 } { 3 } - \sqrt { \frac { 25 } { 4 } } - \frac { 9 } { 2 } ]$$

Evaluate

$$-\frac{187}{6}\approx -31.166666667$$

Solution Steps

Rewrite the square root of the division \frac{25}{4} as the division of square roots \frac{\sqrt{25}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{11}{2}\left(\frac{4}{3}-\frac{5}{2}-\frac{9}{2}\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{4}{3} and \frac{5}{2} to fractions with denominator 6.

$$\frac{11}{2}\left(\frac{8}{6}-\frac{15}{6}-\frac{9}{2}\right)$$

Since \frac{8}{6} and \frac{15}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{2}\left(\frac{8-15}{6}-\frac{9}{2}\right)$$

Subtract 15 from 8 to get -7.

$$\frac{11}{2}\left(-\frac{7}{6}-\frac{9}{2}\right)$$

Least common multiple of 6 and 2 is 6. Convert -\frac{7}{6} and \frac{9}{2} to fractions with denominator 6.

$$\frac{11}{2}\left(-\frac{7}{6}-\frac{27}{6}\right)$$

Since -\frac{7}{6} and \frac{27}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{2}\times \frac{-7-27}{6}$$

Subtract 27 from -7 to get -34.

$$\frac{11}{2}\times \frac{-34}{6}$$

Reduce the fraction \frac{-34}{6} to lowest terms by extracting and canceling out 2.

$$\frac{11}{2}\left(-\frac{17}{3}\right)$$

Multiply \frac{11}{2} times -\frac{17}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\left(-17\right)}{2\times 3}$$

Do the multiplications in the fraction \frac{11\left(-17\right)}{2\times 3}.

$$\frac{-187}{6}$$

Fraction \frac{-187}{6} can be rewritten as -\frac{187}{6} by extracting the negative sign.

$$-\frac{187}{6}$$

Factor

$$-\frac{187}{6} = -31\frac{1}{6} = -31.166666666666668$$