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Let r denote number system radix. The only value(s) of r that satisfy the equation √121_r = 11_r, is/are

1. decimal 10
2. decimal 11
3. decimal 10 and 11
4. any value > 2

Correct answer: any value > 2

Solution

In base r, 121 = r^2+2r+1 = (r+1)^2, so sqrt(121_r) = r+1 = 11_r for every base. The only constraint is that digit '2' must be valid, requiring r>2. Hence any value > 2 works.

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