Question

Verify by calculating square root that√6 is not a rational number

Answer 1

The answer will come in decimals

Answer 2

Let us assume that root 6 is rational.
root 6 = p/q (where p and q are co-primes and q is not equal to zero. )
Squaring on both sides we get
6= p^2/q^2
p^2 = 6q^2...eqn 1.
6 divides p^2
Therefore 6 divides p.
Thus 6 is a factor of p.

p/6 =c
Squaring on both sides we get
p ^2/36 =c^2
p^2 =36 c^2...eqn 2
From eqn 1 and 2
6q^2 =36 c^2
q^2 =6 c^2.
6 divides q^2
Therefore 6 divides q
Thus 6 is a factor of q.

Thus we can say that 6 is a factor of both p and q . But p and q are Co primes.

This contradicts to our assumption.
Hence we can say that root 6 is irrational number.