# Simplifying Radicals: 1/5 inside a square root symbol

#### jramirez23

##### New member
I have a problem with this following problem where I have to simplify a radical expression.

The expression is 1/5 inside a square root symbol.

I know that I have to distribute the square root symbol individually to both the numerator and denominator; so the expression will become a 1 inside a square root symbol OVER 5 inside a square root symbol.

This is where I really become confused. I can't find a way to eliminate the radicand from the denominator so it will simplify.

#### jwpaine

##### Full Member

jramirez23 said:
I have a problem with this following problem where I have to simplify a radical expression.

The expression is 1/5 inside a square root symbol.

I know that I have to distribute the square root symbol individually to both the numerator and denominator; so the expression will become a 1 inside a square root symbol OVER 5 inside a square root symbol.

This is where I really become confused. I can't find a way to eliminate the radicand from the denominator so it will simplify.
$$\displaystyle \sqrt{\frac{1}{5}} = \frac{1}{\sqrt{5}}$$ or if you prefer, you can multiply top and bottom by $$\displaystyle \sqrt{5}$$ to give you $$\displaystyle \frac{\sqrt{5}}{5}$$

Either way is acceptable and equal.

#### jramirez23

##### New member

I'm having another problem, but I get what you have told me.

This new problem that I can't solve is the following:

4 inside a square root symbol
OVER
10 inside a square root symbol

What I did was multiply by the square root of 10 over itself to the original equation.

I then got 40 inside of a square root symbol over 10. This is obviously wrong.

#### Subhotosh Khan

##### Super Moderator
Staff member

jramirez23 said:
I'm having another problem, but I get what you have told me.

This new problem that I can't solve is the following:

4 inside a square root symbol
OVER
10 inside a square root symbol

What I did was multiply by the square root of 10 over itself to the original equation.

I then got 40 inside of a square root symbol over 10. This is obviously wrong.<-- Why do you think so?

Factorize 40 and see if you can take some number outside the radicand sign. Remember

$$\displaystyle \sqrt{8} \,=\, 2\cdot\sqrt{2}$$

Start a new thread with new problem.