Question

show taht √3 is an irrotational. Number

Answer 1

at the contrary let us assume that root over 3 is rational. i.e. we can find integers a and b (b not equal to 0)such that root over3=a/b
Suppose a and b have a common factor other than 1,then we can divide by the common factor and assume that a and b are coprime.
so,root over 3=a
3b^2=a^2(squaring both sides)
so,a^2 is divisible by 3 and a is also divisible by3
so we can write that a=3c,for some integer c 
substituting for a,we get 3b^2=9c^2 i.e.b^2=3c^2
this means that b^2 is divisible by 3 and so b is also divisible by 3
so a and b have at least 3 as a common factor
But this contradicts the fact that a and b are co-prime
This contradiction has arisen because of our wrong assumpsion that root over 3 is rational
so root over 3 is irrational...
HOPE THAT U R CLEAR WITH UR DOUBT NOW...
it would be so kind of u if u mark me brainliest...

Answer 2

Answer:

Step-by-step explanation:

Given in Ncert book of maths