Solve sqrt{((21/2-1/6+2/9)*9)-11/4}

$$\sqrt{ ((2 \frac{ 1 }{ 2 } - \frac{ 1 }{ 6 } + \frac{ 2 }{ 9 } ) \times 9)- \frac{ 11 }{ 4 } }$$

Evaluate

$$\frac{9}{2}=4.5$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\sqrt{\left(\frac{4+1}{2}-\frac{1}{6}+\frac{2}{9}\right)\times 9-\frac{11}{4}}$$

Add 4 and 1 to get 5.

$$\sqrt{\left(\frac{5}{2}-\frac{1}{6}+\frac{2}{9}\right)\times 9-\frac{11}{4}}$$

Least common multiple of 2 and 6 is 6. Convert \frac{5}{2} and \frac{1}{6} to fractions with denominator 6.

$$\sqrt{\left(\frac{15}{6}-\frac{1}{6}+\frac{2}{9}\right)\times 9-\frac{11}{4}}$$

Since \frac{15}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\left(\frac{15-1}{6}+\frac{2}{9}\right)\times 9-\frac{11}{4}}$$

Subtract 1 from 15 to get 14.

$$\sqrt{\left(\frac{14}{6}+\frac{2}{9}\right)\times 9-\frac{11}{4}}$$

Reduce the fraction \frac{14}{6} to lowest terms by extracting and canceling out 2.

$$\sqrt{\left(\frac{7}{3}+\frac{2}{9}\right)\times 9-\frac{11}{4}}$$

Least common multiple of 3 and 9 is 9. Convert \frac{7}{3} and \frac{2}{9} to fractions with denominator 9.

$$\sqrt{\left(\frac{21}{9}+\frac{2}{9}\right)\times 9-\frac{11}{4}}$$

Since \frac{21}{9} and \frac{2}{9} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{21+2}{9}\times 9-\frac{11}{4}}$$

Add 21 and 2 to get 23.

$$\sqrt{\frac{23}{9}\times 9-\frac{11}{4}}$$

Cancel out 9 and 9.

$$\sqrt{23-\frac{11}{4}}$$

Convert 23 to fraction \frac{92}{4}.

$$\sqrt{\frac{92}{4}-\frac{11}{4}}$$

Since \frac{92}{4} and \frac{11}{4} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{92-11}{4}}$$

Subtract 11 from 92 to get 81.

$$\sqrt{\frac{81}{4}}$$

Rewrite the square root of the division \frac{81}{4} as the division of square roots \frac{\sqrt{81}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{9}{2}$$

Factor

$$\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5$$