Consider four-digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?

(1)3

(2)2

(3) 4

(4)1

Any four digit number in which
first two digits are equal and last two digits are also equal will be in the
form 11 × (11a + b) i.e. it will be the multiple of 11 like 1122, 3366, 2244, .
. . .

Now, let the required number be aabb.

Since aabb is a perfect square, the only pair of a and b that satisfy the above mentioned condition is a = 7 and b = 4

Hence, 7744 is a perfect square

Now, let the required number be aabb.

Since aabb is a perfect square, the only pair of a and b that satisfy the above mentioned condition is a = 7 and b = 4

Hence, 7744 is a perfect square

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