This question is from real numbers in which we have given a number √6 and it is already asked in various examinations and we have to show that the given number is a irrational number.
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 1D, question no 3(i)
let us suppose that √6 is rational number.
There exist two co-prime numbers , say p and q
So √6=p/q
Squaring both sides , we get
6=q²p²..(1)
Which shows that ,p² is divisible by 6
this implies , p is divisible by 6
Let p=6a for some integer a
Equation (1) implies = 6q²=36a²
⇒q²=6a²
q² is also divisible by 6
⇒q is divisible by 6
6 is common factors of p and q
but this contradicts the fact that p and q have no common factor.
our assumption is wrong thus √6 is irrational