Question

prove that root3is am irrational number​

Answer 1

Step-by-step explanation:

let root 3 be rational

Assume,root3 equal to p/q (where p and q is a co prime no.)

root3=p/q

root3q=p

squaring both sides

3q^2=p^2......(1)

q^2=p^2/3

if three divides p^2 then it will divide p also

Let p/3=r

again squaring both sides

p^2/9=r^2

From (1)

3q^2/9=r^2

q^2/3=r^2

since 3 divides q square it will divide q also...

but this contradicts the fact that p and q are co primes therefore root 3 is irrational no.

Hope it helps...