How do you simplify a square root of a fraction?

Question

I have seen the following website but I do no fully understand it. Can some one help me.
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http://mathforum.org/library/drmath/view/58152.html

Answer 1

The square root of a fraction is the square root of the numerator over the square root of the denominator.

So if you have sqrt(9/25) that is equal to sqrt(9) / sqrt(25) = 3/5.

That's the easy case where everything works out cleanly.

Let's try another example of sqrt(7/100). This is equal to sqrt(7)/sqrt(100). The bottom works out nicely to give you sqrt(7)/10.

That's about as far as you can go to simplify it, so your answer is
sqrt(7)/10.

Now the other case is where you get a sqrt in the denominator.

sqrt(4/7) = sqrt(4)/sqrt(7) = 2/sqrt(7).

Here we don't like to leave sqrt(7) in the denominator, so multiply top and bottom by another sqrt(7). Notice how this is equal to 1 so you aren't changing the value.

2/sqrt(7) = 2sqrt(7) / sqrt(7)sqrt(7). And what happens if you multiply sqrt(7) * sqrt(7)? You just need to remember that sqrt(a) * sqrt(a) = a. In our case we have sqrt(7) * sqrt(7) = sqrt(49) which is simply 7. So the final answer is:
2 sqrt(7) / 7.

From the website:
sqrt(1/2) = sqrt(1) / sqrt(2) = 1 / sqrt(2).

Multiply top and bottom by sqrt(2):
sqrt(2) / sqrt(2) * sqrt(2)
= sqrt(2) / 2

Answer 2

It's the square root of the numerator over the square root of the denominator. Sqrt(m/n) = sqrt(m)/sqrt(n). If the denominator is not a rational number, you need to rationalize the answer. This is accomplished by multiplying the numerator and denominator by the same thing -- and you pick that thing by figuring out what you can multiply sqrt(n) by so it will be a number without a square root.

Example:
sqrt(5/12) = sqrt(5)/sqrt(12)=sqrt(5)/2(sqrt(3)); then multiply top and bottom by sqrt(3):
sqrt(5)/2(sqrt(3))
=sqrt(3)sqrt(5)/2[(sqrt(3))(sqrt(3))]
=sqrt(15)/[2(3)]
=sqrt(15)/6

Answer 3

ok, the simplified square root wud be the square root of the top number divided by the square root of bottom # ...

Hope this helped!!