Solve sqrt{left|5/2right|}

$$\sqrt{ \left| \frac{ 5 }{ 2 } \right| }$$

Evaluate

$$\frac{\sqrt{10}}{2}\approx 1.58113883$$

Solution Steps

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{5}{2} is \frac{5}{2}.

$$\sqrt{\frac{5}{2}}$$

Rewrite the square root of the division \sqrt{\frac{5}{2}} as the division of square roots \frac{\sqrt{5}}{\sqrt{2}}.

$$\frac{\sqrt{5}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

$$\frac{\sqrt{5}\sqrt{2}}{2}$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{10}}{2}$$