Question

show that (√3-√2) is irrational​

Answer 1

Answer:

Step-by-step explanation:

given: (√3-√2)

R.T.P:let us assume the that (√3-√2) is rational

it can be written in p / q form or a / b form where A and B are co prime

proof: (sobs) squaring on both sides , we get

after squaribg roots get cancel

2 + 3 - 2√6 = (a2/b2)

So,5 - 2√6 = (a2/b2) a rational no.

So, 2√6 = 5- (a2/b2)

Since, 2√6 is an irrational no. and 5 - (a2/b2) is a rational no.

So, my contradiction is wrong.

so our assumtion is wrong

So, (√3 - √2) is an irrational no.

LHS is not = to RHS