ROYal square

Number Theory Level 1

The four digit number aabb is a square. Find it.


The answer is 7744.

Biswaroop Roy by Biswaroop Roy , 25, India

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3 solutions

Raghav Thapar
Mar 5, 2014

The number AABB is divisible by 11 For it to be a perfect square it has to be divisible by 121 and Some other perfect square less than 100 (So that when taken under root they both come out) 121 16=1936 121 25=3025 ... 121*64=7744 This satisfies the given condition

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Harish Manoharan
Mar 5, 2014

1000a+100a+10b+b=11(100a+b) ⟹100a+b must be divisible by 11⟹11|(a+b) as 100≡1(mod99) As 0 ≤ a,b ≤ 9,0 ≤ a + b ≤ 18 ⟹a+b=11 ⟹11(100a+b)=11(100a+11−a)=112(9a+1) So, 9a+1 must be perfect square.The only possibility for a is 7.... 77bb is a perfect square. From this we can say that the root of aabb is between 85-90. Substituting values we see that 88^2 is7744. Thus b is 4. The Answer is 7744.

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I did the same way

Malay Pandey - 7 years, 2 months ago
Xiaoying Qin
Oct 2, 2015

(circles it) I found "it"! say determine the number instead

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