Question

3 r00t 2 is irrational no prove

Answer 1

HEY FRIEND

HERE IS YOUR ANSWER

TO PROVE:

3√2 is an irrational no.


ASSUMPTION :

Let 3√2 is a rational no.


PROOF :

Let 3√2=r

√2=r/3

√2 is an irrational no.

But r/3 is a rational no.

They can't be equal.

So, our supposition is wrong

THEREFORE, 3√2 IS AN IRRATIONAL NO.

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HOPE THIS HELPS YOU ☺

Answer 2

Let us assume √3 is rational
√3=p/q(where p and q have common factor
√3=a/b(where a and b are co-primes
(√3b)^2=a^2
3b^2=a^2
b^2=a^2/3-(1)
If a^2 is divisible by 3
So a will also be divisible by 3
a/3=c
Squaring both sides
(a)^2=3c^2
a^2=9c^2-(2)
From (1) and (2)
a^2=9c^2
3b^2=9c^2
b^2=3c^2
b^2/3=c^2
b^2 is divisible by 3
So b Wil also be divisible by 3
So a and b have common factors 3 so our assumption that a and b are co-primes is wrong
Therefore,√3 is irrational