Expert: Chanda Walker - 3/3/2009

Question
Hi, how are you. I'm having a hard time grasping how to simplify square roots. As easy as it may sound, I'm confused.

I know how to get the square root of smaller numbers and also know how to simplify.

But how would I go about simplifying this for example:

sqrroot (244)

It's not a perfect square root but I know it can break down into

170x2
85x4, I can't really break it down any further. The square root of 4 is 2 so would it be 2 square root (85)?

Thanks in advance.

Answer
You have to factor the number in the square root down.  I suggest you go all the way down to prime numbers but when you get the hang of it, you won't have to do it.  I'll show you an example of how to do this both ways.

All the way down to prime numbers:

Sqrt(244)

Let's factor 244

Always start with the smallest prime numbers.

244 = 2*122

the factor 122 is even so let's factor our another 2.

244 = 2*2*61

Now, 61 is a prime number so we can stop.

Sqrt(244) = Sqrt(2*2*61)

Any numbers that exist in the sqrt twice, can come out once.

Sqrt(244) = 2 Sqrt(61)

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Here is the faster way . . .

244 = 4*61  (you just have to be able to see that which can be tough)

Sqrt(244) = Sqrt(4)*Sqrt(61) = 2 Sqrt(61)