Teacher2Teacher 
Q&A #13682 
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From: Will <spike.hyzer@gmail.com> To: Teacher2Teacher Public Discussion Date: 2007081322:32:46 Subject: Re: ANSWER ME! I know this is over 2 years old but this is how I explain it to my students... The radical is a house and in this house we are throwing a party. Now if the number is "perfect" then we want to throw him out of the house because he thinks he is perfect and thus having a huge ego...and that won't make the party fun. When we kick him out of his house he realizes he isn't wanted anymore and transforms into his alterego(the square root of himself). Same thing goes with number like 20.... 1) figure out larges perfect number that goes into 20 2) rewrite number as a product of that perfect number and its cofactor 3) kick out the perfect people and let the rest stay and party. I also tell them that they only need to check perfect squares which are less than half of the number they are trying to take the square root of. Ex... sqrt(46) we would only have to check 4, 9, and 16 because 1/2(46) = 23
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