Solve =(sqrt{(-3.5/2)^2+(3.25)^2})^2

$$= ( \sqrt { ( - \frac { 3.5 } { 2 } ) ^ { 2 } + ( 3.25 ) ^ { 2 } } ) ^ { 2 }$$

Evaluate

$$13.625$$

Solution Steps

Expand \frac{3.5}{2} by multiplying both numerator and the denominator by 10.

$$\left(\sqrt{\left(-\frac{35}{20}\right)^{2}+3.25^{2}}\right)^{2}$$

Reduce the fraction \frac{35}{20} to lowest terms by extracting and canceling out 5.

$$\left(\sqrt{\left(-\frac{7}{4}\right)^{2}+3.25^{2}}\right)^{2}$$

Calculate -\frac{7}{4} to the power of 2 and get \frac{49}{16}.

$$\left(\sqrt{\frac{49}{16}+3.25^{2}}\right)^{2}$$

Calculate 3.25 to the power of 2 and get 10.5625.

$$\left(\sqrt{\frac{49}{16}+10.5625}\right)^{2}$$

Add \frac{49}{16} and 10.5625 to get \frac{109}{8}.

$$\left(\sqrt{\frac{109}{8}}\right)^{2}$$

The square of \sqrt{\frac{109}{8}} is \frac{109}{8}.

$$\frac{109}{8}$$

Factor

$$\frac{109}{2 ^ {3}} = 13\frac{5}{8} = 13.625$$