How can I find the square root of a number using factor trees?

Question

It's been a long time since using this method, anyone who can refresh my memory would be greatly appreciated. Thanks! :)

Answer 1

First, factor your number into its prime numbers. For example, the number 45 factors into 3x3x5. If you have two of the same number, you have a square. So in the example, you have two 3s (or 9) which is a sqare. You put the sqare-rooted number outside the radical, so 3 and leave the other number(s) inside the radical. So your final answer would be 3 root 5, because the other three got cancelled out of the equation.

Hope this helps!

Another example:
-The square root of 84.
1.) 84 factored is: 2x2x3x7.
2.) Take the twos (or 4-a perfect sqare) out.
3.) Leave 3x7 (21) inside the radical.
4.) The final answer is 2 root 21.

Answer 2

You try to find factors of a number: Number= factor1*factor2. Then you continue with the individual factors until you get to the smallest prime. If you find that factor 1=factor 2, that number is the square root.

Answer 3

For the factor tree it is used when you have a square root of something that does not come out nicely, for example the square root of 8 does not come out nicely. To use the factor tree you are basically simplifying the square root. For example the square root can be broken down, to 2(sqareroot of 2). To do this you take the number inside the square root and start taking multiples out. For this example i took 2 and 4 out, then i took 2 and 2 out for 4, so your left with the square root of (2)(2)(2), which equals 8 if you multiply it out. Then if you see the number repeat itself twice you can bring it out in front. leaving you with 2 square root 2.


Summary:
- take out multiples untill you can no longer shrink it any further
-if a number repeats it self twice you can take it out in front
-if you bring multiple number out just remeber to multiply them

I know this is alot of information and i hoped it helped

Answer 4

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You can take your tree further. the factors of 48 are 2,2,2,2,3 square root of 48 is therefore 2x2xsqrt(3) = 4sqrt(3)

Answer 5

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RE:
How can I find the square root of a number using factor trees?
It's been a long time since using this method, anyone who can refresh my memory would be greatly appreciated. Thanks! :)

Answer 6

105?