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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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Are square numbers always even?
No, but only in the case of the number 1 (12=1) are square numbers odd.
True or false the LCM of two square numbers is another square number?
True.
Are square numbers are always odd?
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
Is the square root of any composite numbers irrational?
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.
What three square numbers that add to another square number?
There are infinitely many possible answers. The smallest set of numbers is (9, 16, 144, 169)
