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If (AB) 2 = CCB then find minimum value of A+B+C. Here, AB is 2 digit and CCB is 3 digit number and A,B,C unequal, A,C not equals 0.

If (AB)2 = CCB then find minimum value of A+B+C. Here, AB is 2 digit and CCB is 3 digit number and A,B,C unequal, A,C not equals 0.

Grade:9

2 Answers

Hasan Naqvi
97 Points
8 years ago
Only if the no has unit digits as 1,5,6,0 will it be possible for it have the same unit digit again. 0 Won't satify it either, as square of no with 0 in unit digit will have 2 zeros.(like 102=100)
 
Also, for the square to be a 3 digit no, AB should be smaller than 32.
SO possible options:
15,16,21,25,26,31
 
Their squares: 225, 256, 441, 625, 676, 961
 
Only two are of form CCB.
So either AB=15(c=2) or 21(c=4)
 
So min value = 4+2+1 = 7
Arivu Selvi
26 Points
2 years ago

And for AB ^ 2 to have the last digit as B, we know that by inspection, B has to be 0, 1, 5 or 6.

(0 * 0, 1 * 1 = 1, 5 * 5 = 25, 6 * 6 = 36).

If we assume A = 1, B =5 , we get 15 * 15 = 225 which is of the format CCB.

Therefore A = 1, B = 5, C = 2.

If we assume A = 2, B = 1 we get 441 which is also of the format CCB.

Therefore A = 2, B = 1, C = 4 is also a solution.

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