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

  1. decimal 10
  2. decimal 11
  3. decimal 10 and 11
  4. any value > 2
asked in Digital Logic by Veteran (68.8k points) | 1.3k views

2 Answers

+27 votes
Best answer

\sqrt{(121)_{r}}=11_{r}

\sqrt{(1*r^{0})+(2*r^{^{1}})+(1*r^{2})}=(1*r^{0})+(1*r^{1})

\sqrt{(1+r)^{^{2}}}=1+r

1+r=1+r

So any integer r satisfies this but r must be > 2 as we have 2 in 121 and radix must be greater than any of the digits. (D) is the most appropriate answer

answered by Boss (6.3k points)
selected by
Please elaborate substitution at some extent. Means how option D is satisfying above relation
Actually there is no need of any substitution.
@Arjun sir plz make RHS also showing base r..plz edit the question..
As we all know radix should be greater than number therefore any value > 2 is right and best answer

D)
why 11 can not be the answer as it is greater than 2
Because it is satisfying radix greater than 2 and 11 is subset of greater than 2 therefore 11 is incomplete answer
+1 vote
As we all know radix should be greater than number therefore any value > 2 is right and best answer

D)
answered by Loyal (4.1k points)


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