Question

Prove that under root3 is irrational

Answer 1

Answer:

Step-by-step explanation:

I have solved this by contradiction method

Let √3 be rational

√3= p\q. ( p and q are co-

prime integers

where q≠0)

3=p^2\q^2 (squaring both side)

3q^2=p^2..................(i)

p^2 is multiple of 3

p will also a multiple of 3

Let p=3m

p^2=9m^2. (Squaring both side)

3q^2=9m^2. (Using i : p^2=3m^2)

q^2=3m^2

q^2 is a multiple of 3

q will also a multiple of 3

Hence , our contradiction is wrong as in the above we have taken p and q are co prime integer but at last we got 3 as common factor . So,√3 is irrational