Problem: Simplify numerical radical terms

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MathClown007

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Aug 16, 2015
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Simplify the expression by removing all factors that are perfect squares from inside the radical.

1. Square Root is 200. Simplify.

2. Let's factor 200 -- [FONT=KaTeX_Main]2×2×5×5×2=2​2​​×5​2​​×2200, equals, 2, times, 2, times, 5, times, 5, times, 2, equals, 2, start superscript, 2, end superscript, times, 5, start superscript, 2, end superscript, times, 2[/FONT]. Therefore, [FONT=KaTeX_Main]200[FONT=KaTeX_Main]200200[/FONT] has at least one factor which is a perfect square ...

With the above formula, I can work out the answer. However, I don't get HOW they derived [/FONT]2×2×5×5×2 to find 200. Did they randomly guess numbers to come up with 200, or is there a method to find out the 200 factor? I would imagine there is. But I have no idea
how it is done. So, can someone please explain HOW to find the numbers that may (or may not) have a perfect square in them. Thank you!
 
MathClown007 said:
Simplify the expression by removing all factors that are perfect squares from inside the radical.

1. Square Root is 200. Simplify.

2. Let's factor 200 -- [FONT=KaTeX_Main]2×2×5×5×2=2​2​​×5​2​​×2200, equals, 2, times, 2, times, 5, times, 5, times, 2, equals, 2, start superscript, 2, end superscript, times, 5, start superscript, 2, end superscript, times, 2[/FONT]. Therefore, [FONT=KaTeX_Main]200[FONT=KaTeX_Main]200200[/FONT] has at least one factor which is a perfect square ...

With the above formula, I can work out the answer. However, I don't get HOW they derived [/FONT]2×2×5×5×2 to find 200. Did they randomly guess numbers to come up with 200, or is there a method to find out the 200 factor? I would imagine there is. But I have no idea
how it is done. So, can someone please explain HOW to find the numbers that may (or may not) have a perfect square in them. Thank you!
Click to expand...

For a quick review, go to:

http://www.mathsisfun.com/prime-factorization.html
 
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