Question

If p is a prime number prove that root p is irrational? It's a 4 mark question

Answer 1

Let √p be a rational number.

Let,√p=a/b,where a and b are integers and b is not = 0.

Then,√p=a/b

Squaring both sides,

(√p)2/1 = (a/b)2

p/1=a2/b2

pb2=a2. (Equation 1)

Therefore,p divides a2.

p divides a also.

Let,a=bq for some integer q.

Put a=bq in equation 1,

pb2=p2q2

b2=pq2

Therefore,p divides b2.

p divides b also.

Thus,p is a common factor of a and b.

So,our assumption is not correct.

Hence,√p is an irrational number.