Question

Prove that 1/2-under root 5 is an irrational

Answer 1

Since root 5 is an irrational no. and any irrational no. divided by rational is an irrationsl no.

Answer 2

Let 1/2-√5 be a rational number,

A rational number can be written in the form of p/q.

1/2-√5 = p/q

√5 = 1/2-p/q

√5 = (q-2p)/2q

p,q are integers then (q-2p)/2q is a rational number,

Then,√5 is also a rational number,

But this contradicts the fact that √5 is an irrational number.

So,our supposition is false.

1/2-√5 is an irrational number.

Hence proved,