Question Number 170205 by otchereabdullai@gmail.com last updated on 18/May/22
![If x is nearer a than b in [a,b], is (√x) necessarily nearer (√a) than (√b) Give a proof of counterexample](Q170205.png)
$$\:\mathrm{If}\:\mathrm{x}\:\mathrm{is}\:\mathrm{nearer}\:\:\:\mathrm{a}\:\:\mathrm{than}\:\:\mathrm{b}\:\:\mathrm{in}\:\left[\mathrm{a},\mathrm{b}\right],\: \\ $$$$\mathrm{is}\:\sqrt{\mathrm{x}}\:\mathrm{necessarily}\:\mathrm{nearer}\:\sqrt{\mathrm{a}}\:\:\mathrm{than}\:\sqrt{\mathrm{b}} \\ $$$$ \\ $$$$\mathrm{Give}\:\mathrm{a}\:\mathrm{proof}\:\mathrm{of}\:\mathrm{counterexample} \\ $$
Answered by floor(10²Eta[1]) last updated on 18/May/22
$$\mathrm{a}=\mathrm{0},\:\mathrm{b}=\mathrm{9},\:\mathrm{x}=\mathrm{4} \\ $$
Commented by otchereabdullai@gmail.com last updated on 18/May/22
$$\mathrm{please}\:\mathrm{can}\:\mathrm{you}\:\mathrm{add}\:\mathrm{the}\:\mathrm{proof}\:\mathrm{for}\:\mathrm{me} \\ $$