Question

Proved that √32 is irrational

Answer 1

Solution:-

Proof

If possible, let √32 be rational and le its simplest from be a/b

Then a and b are integers having no common factor other than 1 and b ≠ 0

Now , √32 = a/b [ squaring on both side]

=> 32 = a²/b²

=> 32b² = a² .....(i)

=> 32 divides a² [ 32 divides 32b² ]

=> 32 divides a

Let a = 32c from some integer c

putting a = 32c in (i) , we get

32b² = 1024 => b² = 32c²

=> 32 divide b²

=> 32 divides b

Thus 32 is a common factor of a and b

But , this contradicts the fact that a and b have no common factor tha 1

the contradiction arises by assuming that √32 is rational

Hence, √32 is irrational