Question

I am lies between 100 &1000 my first two digits make a perfect square (let it be A) and last two digits also make a perfect square.(let it be B).A+B also a perfect square . who I am?​

Answer 1

Answer:

364

Step-by-step explanation:

2-digit perfect square no.s are 16, 25, 36, 49, 64 & 81.

Using Hit & Trial Method, we get 4 different no.s between 100 & 1000 which fulfill the first 2 conditions (i.e. first 2 digits make a perfect square & last 2 digit also make a perfect square), but do they fulfill the 3rd condition? Let's see:

• 164:

                16 (A) & 64 (B) are both perfect squares but the sum of A & B, 16 + 64 = 80, is NOT a perfect square (i.e. 8.94).

• 364:

                 36 (A) & 64 (B) are both perfect squares but the sum of A & B, 36 + 64 = 100, IS a perfect square (i.e. 10).

• 649:

                64 (A) & 49 (B) are both perfect squares but the sum of A & B, 64 + 49 = 113, is NOT a perfect square (i.e. 10.63).

• 816:

                81 (A) & 16 (B) are both perfect squares but the sum of A & B, 81 + 16 = 97, is NOT a perfect square (i.e. 9.84).

Hence we can conclude that "I am 364".

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