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How many positive even multiples of 3 are perfect squares and less than 1 million?
Wiki User
∙ 14y ago
Answer = 166
When a multiple of 3 is a perfect square then we can write 3m = y2
As m is an even number then m = 2n and 6n = y2
The prime factors of 6 are 2 and 3 therefore n must also contain these prime factors as y2 can only have prime factors with even numbered exponents.
We can now write 6n = 6 x 6p = 36p = y2
As 36 = 62 then p must also be a square number and we can write p = q2
Therefore p = 1(12),4(22),9(32),16(42) etc.....and the relevant squares are 1 x 36 = 62, 4 x 36 = 144 (122), 9 x 36 = 324 (182), 16 x 36 = 576 (242) .....and so on.
1000000 ÷ 36 = 27777.78
√27777.78 = 166.66 →166 rounded to the integer below - and which is the answer to the question.
Wiki User
∙ 14y ago
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