Question

prove √3 is irrational
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Answer 1

Answer:

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Answer 2

To prove: √3 as irrational

Let us assume √3 as rational

So, it can be written as p/q form

√3= p/q

√3q= p

Squaring on both sides

(√3q)^2=p^2

3q^2= p^2

p^2/3=q^2

Here, 3 divides p^2

and 3 divides p

---------(1)

Hence

p/3=r (r is some integer)

p=3r

We know that

3q^2=p^2

3q^2=(3r)^2

3q^2=9r^2

q^2=3r^2

r^2=q^2/3

Here, 3 divides q^2

and 3 divides q

--------------(2)

From (1) and (2)

3 divides both p and q

So, 3 is factor of p and q

but p and q have factor 3

so p and q are not co-primes

Our assumption is wrong

By contradiction

√3 is irrational.

Hence proved