Question

Simplify

Short answer

The final answer is $\sqrt{\frac{5}{2}}=\frac{\sqrt{10}}{2}.$

Step-by-step solution

Step 1. Given information:

The given expression is $\sqrt{\frac{5}{2}}$ .

Step 2. Concept use.

Separate the factors into their own square roots.

Dividing by its denominator.

Step 3. Applying the concept.    

Dividing by in its numerator and denominator.

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

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

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

Since square root is positive quantity so we neglect negative sign.

Therefore, the simplified form is $\sqrt{\frac{5}{2}}=\frac{\sqrt{10}}{2}.$