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

$4 \textless\ k\pi \textless\ 5==\textgreater\ \dfrac{4}{\pi} \textless\ k\textless\ \dfrac{5}{\pi}\\ ==\textgreater\ 1.2732... \textless\ k \textless\ 1.5915....\\ ==\textgreater\ 1.27 \textless\ k \textless\ 1.60\\ ==\textgreater\ \dfrac{128}{100} \textless\ k \textless\ \dfrac{160}{100} \\ example\ k=\dfrac{129}{100}==\textgreater\ \dfrac{129*\pi}{100}=4.05265...\\ k=\dfrac{159}{100}==\textgreater\ \dfrac{159*\pi}{100}=4.9951....$