14 votes 14 votes Which of the following is true ? $\sqrt{3}+\sqrt{7}=\sqrt{10}$ $\sqrt{3}+\sqrt{7}\leq \sqrt{10}$ $\sqrt{3}+\sqrt{7}< \sqrt{10}$ $\sqrt{3}+\sqrt{7}> \sqrt{10}$ Quantitative Aptitude quantitative-aptitude isro2016 inequality + – ManojK asked Jul 4, 2016 edited Dec 8, 2022 by Lakshman Bhaiya ManojK 5.0k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 32 votes 32 votes Ans D $ (\sqrt 3+ \sqrt 7)^2 = (\sqrt 3)^2 + 2 . \sqrt 3. \sqrt 7 + (\sqrt 7 )^2 = 3+2\sqrt {21}+7 =10+ 2\sqrt {21}$ $(\sqrt {10})^2 =10 < 10 +2 \sqrt {21}$ So $\sqrt 3+ \sqrt 7 > \sqrt {10}$ sh!va answered Jul 4, 2016 selected Jul 4, 2016 by Arjun sh!va comment Share Follow See 1 comment See all 1 1 comment reply Rohit Kumar 2 commented Apr 17, 2018 reply Follow Share Shiva, you are right in solving this question. I'm happy to read your solution. Here I want to share another method to solve this question. almost, everyone know root(4) = 2 root(9) = 3 root(16) = 4 now, little perception required here. based on above data values, root(3)<2 root(7)<3 and greater than 2 root(10)<4 and greater than 3 now, taking extreme values on lhs and rhs, we arrive at conclusion that lhs>rhs therefore, answer is d. 0 votes 0 votes Please log in or register to add a comment.
13 votes 13 votes take log on each term..then it will be ..log(√3)+log(√7)=log(√10) ..1/2log(3)+1/2log(7)=1/2(log10) (divide by 1/2) ..log 3+ log 7=log 10 [log a +log b= log(ab)] ..log(21)>log10 so D is the ans asu answered Jul 4, 2016 asu comment Share Follow See all 9 Comments See all 9 9 Comments reply Show 6 previous comments srestha commented Jul 4, 2016 reply Follow Share how? 10 + 10 = 20 log 10 + log 10 = log 20 which formula? 0 votes 0 votes LeenSharma commented Jul 4, 2016 reply Follow Share yes,@srestha i was totally wrong here. Thank You :) 1 votes 1 votes LeenSharma commented Jul 4, 2016 reply Follow Share It should be 10 + 10 = 20log (10 + 10) = log 20 log (10 * (1+1) ) = log 20 log (10 * (2) ) = log 20 log 10 + log 2 = log (10*2) log 10 + log 2 = log 10 + log 2 I think i am right now. 1 votes 1 votes Please log in or register to add a comment.
2 votes 2 votes answer should be (D) cse23 answered Jul 4, 2016 cse23 comment Share Follow See all 0 reply Please log in or register to add a comment.