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Conjectures about Square Numbers4 9 16 25 36 49 64 81 100A conjecture is a statement that might be true about a pattern or relationship. Investigate whether these conjectures about square numbers seem to be true or false by trying examples with different numbers. Record carefully what you do at each stage. If you think the conjecture is true, try to explain why.If you think the conjecture is false, try to find a counterexample.If you are not sure about one of them, try one of the others and come back to it later.As you are working on this you may think of some conjectures of your own about square numbers. If so you can investigate them and record the details.The square of every even number is a multiple of 4.The square of every odd number is odd.A square number with a units digit of 1 is the square of a number with a units digit of 1.A square number with a units digit of 5 is the square of a number with a units digit of 5.121 is the only palindromic square number with 3 digits (‘palindromic’ means the number is the same when written backwards)The sum of a number and its square is always even.Every number of the form 8n + 1 is a square number.The square of every odd number is of the form 8n + 1.The 10s digit of an odd square number is always even. The 10s digit of an even square number is always odd. The square of a number is greater than the result of multiplying it by 10. The sum of the squares of three consecutive numbers is always 1 less than a multiple of 3. ................
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