+30 Find the smallest positive integer n ≥ 100 such that {√n} >1/2.
Note: for a real number x, {x} = x − \(\lfloor x \rfloor\)denotes the fractional part of x.
You can do this by trial and error. Since \(\sqrt{110 } \ is\ approximately\ 10.4880884817 \) with fractiona part equal to
\(10.4880884817 -10 = 0.4880884817<0.5\),
and \(\sqrt{111}\) is approximately \(10.5356537529 \)with fractional part equal to
\(10.5356537529 -10=0.5356537529>0.5\),
n = 111 must be the number you are looking for.
You can do this by trial and error. Since \(\sqrt{110 } \ is\ approximately\ 10.4880884817 \) with fractiona part equal to
\(10.4880884817 -10 = 0.4880884817<0.5\),
and \(\sqrt{111}\) is approximately \(10.5356537529 \)with fractional part equal to
\(10.5356537529 -10=0.5356537529>0.5\),
n = 111 must be the number you are looking for.
