14 votes 14 votes Define the value of $r$ in the following: $\sqrt {(41)_{r}} = (7)_{10}$ Digital Logic gate1988 digital-logic normal number-representation descriptive + – go_editor asked Dec 11, 2016 recategorized Apr 16, 2021 by Lakshman Bhaiya go_editor 2.2k views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply target2017 commented Dec 11, 2016 reply Follow Share Is the question: $\sqrt{41}_r=7_{10}$ 1 votes 1 votes go_editor commented Dec 13, 2016 reply Follow Share Yes, Now corrected. Please check. 0 votes 0 votes Please log in or register to add a comment.
Best answer 26 votes 26 votes $\sqrt{(41)_r} = (7)_{10}$ Squaring both sides we get $(41)_r = (49)_{10}$ $\implies 4r+1 = 10\times 4+9$ $\implies 4r = 48$ $\implies r = 12$ focus _GATE answered Dec 11, 2016 edited Jan 30 by Hira Thakur focus _GATE comment Share Follow See all 4 Comments See all 4 4 Comments reply air1ankit commented Jan 2, 2018 reply Follow Share 4r+1=40+9 how this line is coming 0 votes 0 votes focus _GATE commented Feb 2, 2018 reply Follow Share r0 * 1 +r1 *4 =1 +4r rt ?? 0 votes 0 votes Shiva Sagar Rao commented Sep 11, 2019 i edited by Shiva Sagar Rao Dec 11, 2020 reply Follow Share Be careful while applying squaring on both sides. Eg: If question is $\sqrt{(41)_{r}} = (14)_{8}$ then after applying squaring on both sides $(41)_{r} = (196)_{8}$. But this is wrong because $(14^2)_{8} = (220)_{8}$ 4 votes 4 votes Abhrajyoti00 commented Jan 5, 2023 reply Follow Share @Shiva Sagar Rao Yes, first convert all in decimal number system. Then apply squares. Even in this question:- $\sqrt{41_r} = 7_{10}$ $=>\sqrt{4r+1} = 7_{10}$ $=>4r+1 = 49$ $r = 12$ 2 votes 2 votes Please log in or register to add a comment.