Solve (7/4-2)sqrt{5/3-1/9}

$$( \frac { 7 } { 4 } - 2 ) \sqrt { \frac { 5 } { 3 } - \frac { 1 } { 9 } }$$

Evaluate

$$-\frac{\sqrt{14}}{12}\approx -0.311804782$$

Solution Steps

Convert 2 to fraction \frac{8}{4}.

$$\left(\frac{7}{4}-\frac{8}{4}\right)\sqrt{\frac{5}{3}-\frac{1}{9}}$$

Since \frac{7}{4} and \frac{8}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-8}{4}\sqrt{\frac{5}{3}-\frac{1}{9}}$$

Subtract 8 from 7 to get -1.

$$-\frac{1}{4}\sqrt{\frac{5}{3}-\frac{1}{9}}$$

Least common multiple of 3 and 9 is 9. Convert \frac{5}{3} and \frac{1}{9} to fractions with denominator 9.

$$-\frac{1}{4}\sqrt{\frac{15}{9}-\frac{1}{9}}$$

Since \frac{15}{9} and \frac{1}{9} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{4}\sqrt{\frac{15-1}{9}}$$

Subtract 1 from 15 to get 14.

$$-\frac{1}{4}\sqrt{\frac{14}{9}}$$

Rewrite the square root of the division \sqrt{\frac{14}{9}} as the division of square roots \frac{\sqrt{14}}{\sqrt{9}}.

$$-\frac{1}{4}\times \frac{\sqrt{14}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$-\frac{1}{4}\times \frac{\sqrt{14}}{3}$$

Multiply -\frac{1}{4} times \frac{\sqrt{14}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\sqrt{14}}{4\times 3}$$

Multiply 4 and 3 to get 12.

$$\frac{-\sqrt{14}}{12}$$