Solve ({left(2/3right)}^2+{left(3/2right)}^2

$$( { \left( \frac{ 2 }{ 3 } \right) }^{ 2 } + { \left( \frac{ 3 }{ 2 } \right) }^{ 2 }$$

Evaluate

$$\frac{97}{36}\approx 2.694444444$$

Solution Steps

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

$$\frac{4}{9}+\left(\frac{3}{2}\right)^{2}$$

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

$$\frac{4}{9}+\frac{9}{4}$$

Least common multiple of 9 and 4 is 36. Convert \frac{4}{9} and \frac{9}{4} to fractions with denominator 36.

$$\frac{16}{36}+\frac{81}{36}$$

Since \frac{16}{36} and \frac{81}{36} have the same denominator, add them by adding their numerators.

$$\frac{16+81}{36}$$

Add 16 and 81 to get 97.

$$\frac{97}{36}$$

Factor

$$\frac{97}{2 ^ {2} \cdot 3 ^ {2}} = 2\frac{25}{36} = 2.6944444444444446$$