Please elaborate substitution at some extent. Means how option D is satisfying above relation

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+17 votes

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

- decimal $10$
- decimal $11$
- decimal $10$ and $11$
- any value > $2$

+31 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**

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