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How many positive integers less than 2008 have an even number of divisors?
There are 1,963 such integers. Every factor of a number has a pair. The only time there will be an odd number of factors is if one factor is repeated, ie the number is a perfect square. So the question is really asking: how many positive integers less than 2008 (in the range 1 to 2007) are not perfect squares. √2007 = 44 and a bit (it lies between 44 and 45) So there are 44 integers less than (or equal to) 2007 which are perfect squares → 2007 - 44 = 1963 integers are not perfect squares in the range 1-2007 and have an even number of factors (divisors).
The square root of 83 lies between what number?
Between which two consecutive whole numbers does \sqrt{83} 83 lie? Fill out the sentence below to justify your answer and use your mouse to drag \sqrt{83} 83 to an approximately correct location on the number line.
Which number lies between 0.5 and 0.65?
0.500001
What number lies between 9.55 9.56?
9.55.5
What number lies halfway between 1.64 and 1.7?
1.67
