Question

show that 3.1245454545... is a rational number​

Answer 1

ANSWER

Let suppose 5​,→ rational number 

so 5​ van be written as a/b 

wherre both a q b are not co-prime 

5​=ba​

5​b=a

5b2=a2

5a2​=b2   ......... 1

by theorem if 5 devises a2 then it will decide a also 

Hence we  can say 

5a​=c   (c=any integer)

a=5c ...... 2

by 1 2

25c2=5B2

b2=5c2

5b2​=c2


By theorem if 5 devises b2 then it will all divide b 

So here 5 is a factor of both a and b 

Therefore a and b are not co-prime 

so by contradiction 

5​ is irrational 

and we can prove (a−5​) also by this way