Solve [(2-1/4)*(3-1/2)]^2-sqrt{4/9}=

$$[ ( 2 - \frac { 1 } { 4 } ) \cdot ( 3 - \frac { 1 } { 2 } ) ] ^ { 2 } - \sqrt { \frac { 4 } { 9 } } =$$

Evaluate

$$\frac{3547}{192}\approx 18.473958333$$

Solution Steps

Subtract \frac{1}{4} from 2 to get \frac{7}{4}.

$$\left(\frac{7}{4}\left(3-\frac{1}{2}\right)\right)^{2}-\sqrt{\frac{4}{9}}$$

Subtract \frac{1}{2} from 3 to get \frac{5}{2}.

$$\left(\frac{7}{4}\times \frac{5}{2}\right)^{2}-\sqrt{\frac{4}{9}}$$

Multiply \frac{7}{4} and \frac{5}{2} to get \frac{35}{8}.

$$\left(\frac{35}{8}\right)^{2}-\sqrt{\frac{4}{9}}$$

Calculate \frac{35}{8} to the power of 2 and get \frac{1225}{64}.

$$\frac{1225}{64}-\sqrt{\frac{4}{9}}$$

Rewrite the square root of the division \frac{4}{9} as the division of square roots \frac{\sqrt{4}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{1225}{64}-\frac{2}{3}$$

Subtract \frac{2}{3} from \frac{1225}{64} to get \frac{3547}{192}.

$$\frac{3547}{192}$$

Factor

$$\frac{3547}{2 ^ {6} \cdot 3} = 18\frac{91}{192} = 18.473958333333332$$