Solve 2.5^2+{left(frac{sqrt{3}}{2}right)}^2

$${ 2.5 }^{ 2 } + { \left( \frac{ \sqrt{ 3 } }{ 2 } \right) }^{ 2 }$$

Evaluate

$$7$$

Solution Steps

Calculate 2.5 to the power of 2 and get 6.25.

$$6.25+\left(\frac{\sqrt{3}}{2}\right)^{2}$$

To raise \frac{\sqrt{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$6.25+\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}$$

The square of \sqrt{3} is 3.

$$6.25+\frac{3}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$6.25+\frac{3}{4}$$

Add 6.25 and \frac{3}{4} to get 7.

$$7$$

Factor

$$7$$