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

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

Evaluate

$$1$$

Solution Steps

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

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

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

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

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

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

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

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

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

$$\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$1$$

Factor

$$1$$