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

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

Evaluate

$$12.3125$$

Solution Steps

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

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

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

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

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

$$\sqrt{\frac{49}{16}}+3.25^{2}$$

Rewrite the square root of the division \frac{49}{16} as the division of square roots \frac{\sqrt{49}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{7}{4}+3.25^{2}$$

Calculate 3.25 to the power of 2 and get 10.5625.

$$\frac{7}{4}+10.5625$$

Add \frac{7}{4} and 10.5625 to get \frac{197}{16}.

$$\frac{197}{16}$$

Factor

$$\frac{197}{2 ^ {4}} = 12\frac{5}{16} = 12.3125$$