Solve 7.5^2+{left(frac{5sqrt{3}}{2}right)}^2

$${ 7.5 }^{ 2 } + { \left( \frac{ 5 \sqrt{ 3 } }{ 2 } \right) }^{ 2 }$$

Evaluate

$$75$$

Solution Steps

Calculate 7.5 to the power of 2 and get 56.25.

$$56.25+\left(\frac{5\sqrt{3}}{2}\right)^{2}$$

To raise \frac{5\sqrt{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$56.25+\frac{\left(5\sqrt{3}\right)^{2}}{2^{2}}$$

Expand \left(5\sqrt{3}\right)^{2}.

$$56.25+\frac{5^{2}\left(\sqrt{3}\right)^{2}}{2^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$56.25+\frac{25\left(\sqrt{3}\right)^{2}}{2^{2}}$$

The square of \sqrt{3} is 3.

$$56.25+\frac{25\times 3}{2^{2}}$$

Multiply 25 and 3 to get 75.

$$56.25+\frac{75}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$56.25+\frac{75}{4}$$

Add 56.25 and \frac{75}{4} to get 75.

$$75$$

Factor

$$3\times 5^{2}$$