Question

show with steps that root 2is not rational number

Answer 1

If we substitute a = 2k into the original equation 2 = a2/b2, this is what we get:

2=(2k)2/b2
2=4k2/b2
2*b2=4k2
b2=2k2

Answer 2

So let is assume tat √2 is a rational number.

√2=a÷b (a,b are integers n b is not equal to zero)
2=a^2 ÷ b^2
2b^2 =a^2

As b^2 is divisible by. 2 then b is also divisible by 2.

let a^2 = 4c^2
a =2c
Thus 2b^2=4c^2=b^2 =2c^2(2,n 4 gets cancelled )
then b = 2c

This contradicts our assumption tat a,b are rational numbers n have a common factor 2.


threfore a n b are not rational numbers since they do not hv any common factor other than unity or 1.(They have 2 as a common factor)