Think of their prime factorizations. A squared number will always have paired prime factors. When they have no prime factors in common, like 4 (2 x 2) and 9 (3 x 3), the LCM will be their product, 2 x 2 x 3 x 3 or 36 (6 squared). When they have prime factors in common, like 36 (2 x 2 x 3 x 3) and 225 (3 x 3 x 5 x 5), the LCM will still have paired factors: 2 x 2 x 3 x 3 x 5 x 5 or 900 (30 squared)
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No, but only in the case of the number 1 (12=1) are square numbers odd.
True.
No. The square of an odd number will be odd and the square of an even number will be even.Examples:5x5=2511x11=12115x15=2254x4=168x8=6416x16=256
The square root of a composite number is not always an irrational number. e.g. 4 is a composite number and its square root is 41/2 = 2, which is rational number.
There are infinitely many possible answers. The smallest set of numbers is (9, 16, 144, 169)