Question

Simplify

$\sqrt{\frac{1}{5}}$

Short answer

The final answer is $\sqrt{\frac{1}{5}}=\frac{1}{\sqrt{5}}.$

Step-by-step solution

Step 1. Given information:

The given expression is $\sqrt{\frac{1}{5}}$.

Step 2. Concept used.

We have to find the factors of the given numbers in the fraction separately.

Separate the factors into their own square roots.

Step 3. Applying the concept.    

Now, as we know that the factor of $1=1$and $5=5$.

$\sqrt{\frac{1}{5}}=\frac{1}{\sqrt{5}}$

$=\pm \frac{1}{\sqrt{5}}$

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

Therefore, the simplified form is $\sqrt{\frac{1}{5}}=\frac{1}{\sqrt{5}}.$