Question

Prove 1/5+√3 is an irrational number

Answer 1

Answer:

Let's assume 1/5+root3 is rational.

As 1/5+root3 is rational, 1/5+root3=p/q where पी and q are Co-prime numbers and their HCF is 1.

1/5+root3=p/q

root3=p/q-1/5

As we know the root of any prime number is irrational and root3 is irrational.

So, our assumption made was wrong and an irrational cannot be divided by a rational.

Hence, our assumption made was wrong and,

1/5+root3 is irrational.