Solve (5/2sqrt{3})^2+(21/2)^2

$$( \frac { 5 } { 2 } \sqrt { 3 } ) ^ { 2 } + ( \frac { 21 } { 2 } ) ^ { 2 }$$

Evaluate

$$129$$

Solution Steps

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

$$\left(\frac{5}{2}\right)^{2}\left(\sqrt{3}\right)^{2}+\left(\frac{21}{2}\right)^{2}$$

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\frac{25}{4}\left(\sqrt{3}\right)^{2}+\left(\frac{21}{2}\right)^{2}$$

The square of \sqrt{3} is 3.

$$\frac{25}{4}\times 3+\left(\frac{21}{2}\right)^{2}$$

Multiply \frac{25}{4} and 3 to get \frac{75}{4}.

$$\frac{75}{4}+\left(\frac{21}{2}\right)^{2}$$

Calculate \frac{21}{2} to the power of 2 and get \frac{441}{4}.

$$\frac{75}{4}+\frac{441}{4}$$

Add \frac{75}{4} and \frac{441}{4} to get 129.

$$129$$

Factor

$$3\times 43$$