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

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

Evaluate

$$\frac{\sqrt{122}}{2}\approx 5.522680509$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

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

Calculate 5 to the power of 2 and get 25.

$$\sqrt{4+25+\frac{3}{2}}$$

Add 4 and 25 to get 29.

$$\sqrt{29+\frac{3}{2}}$$

Convert 29 to fraction \frac{58}{2}.

$$\sqrt{\frac{58}{2}+\frac{3}{2}}$$

Since \frac{58}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{58+3}{2}}$$

Add 58 and 3 to get 61.

$$\sqrt{\frac{61}{2}}$$

Rewrite the square root of the division \sqrt{\frac{61}{2}} as the division of square roots \frac{\sqrt{61}}{\sqrt{2}}.

$$\frac{\sqrt{61}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{61}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{61}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{61}\sqrt{2}}{2}$$

To multiply \sqrt{61} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{122}}{2}$$