Question 252285: How many numbers from 1 to 1 million, inclusive, are NOT perfect squares or perfect cubes?
a. 998,000 b. 998,830 c. 998,900 d. 998,910 e. 999,000
Answer by drk(1908)   (Show Source):
You can put this solution on YOUR website! First lets look at perfect squares: 1^2, 2^2, 3^2, 4^2, . . . , 1000^2 are all perfect squares <= 1 million, inclusive.
Second, let's look at perfect cubes: 1^3, 2^3, 3^3, 4^3, . . . , 100^3 are all perfect cubes less than or equal to 1 million inclusive.
So we have 1100 so far.
But notice that some perfect squares are perfect cubes. That occurs at perfect sixth powers. we have to eliminate this overlap. Perfect sixth powers are: 1^6, 2^6, 3^6, . . . , 10^6 are all perfect sixth powers less than or equal to 1 million inclusive.
So, 1 million - 1100 +10 = 998,910.
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