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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 (59.6k points)
edited by | 1.8k views

2 Answers

+32 votes
Best answer

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

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

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

$1+r=1+r$

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

answered by Loyal (6.1k points)
selected by
+1
Please elaborate substitution at some extent. Means how option D is satisfying above relation
+3
Actually there is no need of any substitution.
+2
@Arjun sir plz make RHS also showing base r..plz edit the question..
+2
As we all know radix should be greater than number therefore any value > 2 is right and best answer

D)
0
why 11 can not be the answer as it is greater than 2
+1
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 Active (3.7k points)
0
Nice answer.correct logic.


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