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

The Gateway to Computer Science Excellence

First time here? Checkout the FAQ!

x

+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**

- All categories
- General Aptitude 1.3k
- Engineering Mathematics 5.4k
- Digital Logic 2.1k
- Programming & DS 3.9k
- Algorithms 3.4k
- Theory of Computation 4.2k
- Compiler Design 1.6k
- Databases 3.1k
- CO & Architecture 2.7k
- Computer Networks 3.1k
- Non GATE 1.1k
- Others 1.4k
- Admissions 501
- Exam Queries 448
- Tier 1 Placement Questions 19
- Job Queries 62
- Projects 12

37,963 questions

45,465 answers

131,321 comments

48,376 users