Solve 3sqrt{9{left(1-frac{1/3right)}^2-3/2}{2+1/2}}

$$3 \sqrt{ \frac{ 9 { \left(1- \frac{ 1 }{ 3 } \right) }^{ 2 } - \frac{ 3 }{ 2 } }{ 2+ \frac{ 1 }{ 2 } } }$$

Evaluate

$$3$$

Solution Steps

Subtract \frac{1}{3} from 1 to get \frac{2}{3}.

$$3\sqrt{\frac{9\times \left(\frac{2}{3}\right)^{2}-\frac{3}{2}}{2+\frac{1}{2}}}$$

Calculate \frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$3\sqrt{\frac{9\times \frac{4}{9}-\frac{3}{2}}{2+\frac{1}{2}}}$$

Multiply 9 and \frac{4}{9} to get 4.

$$3\sqrt{\frac{4-\frac{3}{2}}{2+\frac{1}{2}}}$$

Subtract \frac{3}{2} from 4 to get \frac{5}{2}.

$$3\sqrt{\frac{\frac{5}{2}}{2+\frac{1}{2}}}$$

Add 2 and \frac{1}{2} to get \frac{5}{2}.

$$3\sqrt{\frac{\frac{5}{2}}{\frac{5}{2}}}$$

Divide \frac{5}{2} by \frac{5}{2} to get 1.

$$3\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$3\times 1$$

Multiply 3 and 1 to get 3.

$$3$$

Factor

$$3$$