HELP MEEE PLEASEEEEE Which number is the greatest: √36, 6.34 (4 repeating only), 6.34 (34 repeating)? Explain why
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Answers:
25 = 5*5 which is the same as 25 = 5^2
100 = 2*2*5*5 which is the same as 100 = 2^2*5^2
16 = 2*2*2*2 which is the same as 16 = 2^4
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Explanation:
To find the prime factorization of 25, we divide by prime numbers. We see that 25/2 = 12.5 isn't a whole number, and neither is 25/3 = 8.33 (approx). But 25/5 = 5 is a whole number. The result is a prime number so we can stop here. This shows that 25 = 5*5 = 5^2
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We'll do the same for 100 as well. Start with dividing over 2
100/2 = 50
50/2 = 25
we can't do 25/2 as mentioned earlier, but we can say 25/5 = 5
So basically 100 = 2*2*25 = 2*2*5*5 = 2^2*5^2
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The same will happen with 16 as well. We divide by 2 until we arrive at a prime number result
16/2 = 8
8/2 = 4
4/2 = 2
We have three 2's as denominators and that last result 2 is included in the set of prime factors as well to say 16 = 2*2*2*2 = 2^4
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The factor tree for each is shown below. For something like 100, there are a few ways to draw out the tree. The same applies for 16 as well.
