Question

Prove thar 3+2✓5is irrational

Answer 1

Answer:

Let's assume that 3+2root5 is rational.

As 3+2root5 is rational, 3+2root5=p/q where पी and q are Co-prime numbers and their HCF is 1.

3+2root5=p/q

2root5=p/q-3

2root5=p/q-3/q (LCM is q)

2root5=p-3/q

root5=p-3/2q

As we know root of any prime number is irrational and root5 is irrational.

Hence an irrational cannot be divided by a rational and,

3+2root5 is irrational.