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The number of integers `a`(1≤a≤200) such that a^a is a perfect square(A)105 (b)103 (c)107(d)109

The number of integers `a`(1≤a≤200) such that a^a is a perfect square(A)105 (b)103 (c)107(d)109

Grade:11

1 Answers

Pranit Mehta
24 Points
7 years ago
All even values of a will result in a^a being a perfect square. It is so because, for a number to be a perfect square, the power of the number should be able to be represented as a multiple of 2.This has 100 cases!Secondly, we need to consider those numbers such that a is odd but a perfect square so that the power is a multiple of 2. This has 1,9,25,49,81,121,169.This has 7 cases!Hence the total sums up to 107.

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