Question

Prove that √5 is irrational and hence show that 3 + √5 is also irrational.

Answer 1

Answer:

Say, √5 is a rational number. ∴ It can be expressed in the form p/q where p,q are co-prime integers. Hence, p,q have a common factor 5. ... Therefore √5+3 is also irrational because sum of a rational and an irrational number is always an irrational number.

Answer 2

Answer:

Step-by-step explanation:

Say, √5 is a rational number. ∴ It can be expressed in the form p/q where p,q are co-prime integers. Hence, p,q have a common factor 5. Therefore √5+3 is also irrational because sum of a rational and an irrational number is always an irrational number.