Question

Write three irrational numbers between 4 and 5.

Answer 1

Hello,

1) one way
4<x<5 ==>16<x²<25
if x²=17==>x=√17=4.123.....
if x²=18==>x=√18=4.242...
if x²=19==>x=√19=4.358...
...
if x²=24==>x=√24=4.898...

2) an other way

4<x<5 ==>64<x³<125

if x³=65 then ∛65=4.020...
...
if x³=124 then ∛124=4.986...

3) an other way


`4 \textless\ k\pi \textless\ 5==\textgreater\ (4)/(\pi) \textless\ k\textless\ (5)/(\pi)\\ ==\textgreater\ 1.2732... \textless\ k \textless\ 1.5915....\\ ==\textgreater\ 1.27 \textless\ k \textless\ 1.60\\ ==\textgreater\ (128)/(100) \textless\ k \textless\ (160)/(100) \\ example\ k=(129)/(100)==\textgreater\ (129*\pi)/(100)=4.05265...\\ k=(159)/(100)==\textgreater\ (159*\pi)/(100)=4.9951....\\`