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Which one of the following numbers is not a square of any natural number?

How many factors of the number 4000 are perfect squares ?

How many factors of the number 4000 are perfect squares ?

Is 1 a square number? How can you tell?

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(i) Find the number of reatangles of any size in a chess board (ii) Find the number of squares of any size in a rectangle of size 8xx 5 .

mn squares of equal size are arranged to form a rectangle of dimension m by n, where m and n are natural numbers. Two square will be called neighbors if they have exactly one common side. A number is written in each square such that the number written in any square is the arithmetic mean of the numbers written in its neighboring squares. Show that this is possible only if all the numbers used are equal.

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