Solve sqrt{(5/2)^2+(6/4sqrt{3})^2}

$$\sqrt { ( \frac { 5 } { 2 } ) ^ { 2 } + ( \frac { 6 } { 4 } \sqrt { 3 } ) ^ { 2 } }$$

Evaluate

$$\sqrt{13}\approx 3.605551275$$

Solution Steps

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

$$\sqrt{\frac{25}{4}+\left(\frac{6}{4}\sqrt{3}\right)^{2}}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

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

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

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

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\sqrt{\frac{25}{4}+\frac{9}{4}\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{\frac{25}{4}+\frac{9}{4}\times 3}$$

Multiply \frac{9}{4} and 3 to get \frac{27}{4}.

$$\sqrt{\frac{25}{4}+\frac{27}{4}}$$

Add \frac{25}{4} and \frac{27}{4} to get 13.

$$\sqrt{13}$$