If aabb is a perfect square. Find the value of a+b
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Note that a a b b = 1 1 ∗ ( 1 0 0 a + b ) . Then ( 1 0 0 a + b ) must be divisible by 11. Since 1 1 ∣ ( 1 0 0 a + b ) , the sum of its odd digits minus the sum of its even digits must be divisible by 11. This implies that 1 1 ∣ ( a + b ) . Since a , b ≤ 9 , a + b ≤ 1 8 leaving a + b = 1 1 as our answer.