Question

prove that under root 5 is an irrational number also prove that 3 + under root 5, 3- under root 5, 3/ under root 5 ,3+2 underroot 5 it is also irrational

Answer 1

yes under root 5 is an irrational number because the value of the under root 5 is an irrational number so too as we know that when a rational and irrational number is added the value is irrational so 3 + root 5 is an irrational number second case 3 minus root 5 in this case it is also an irrational number because as the case states that if we subtract and irrational from a rational number it gives us irrational number so it is under rational number in the third case 3 + 2 under root 5 is an irrational number because it is same as the first case is 3 + root 5 in this case it is just 5 + root 5 so it is also an irrational number hope it helps you and please don't forget to mark it thank you

Answer 2

✓5 is an irrational number as it's decimal expansion is non-terminating and non-recurring.
In the property given it is mentioned that any operation between a rational and irrational number is an irrational answer.
Any operation between two irrational number can be rational or irrational.

Here,
3 is an rational number so,
3+✓5 is an irrational
3-✓5 is an irrational
3/✓5 is an irrational
3+2✓5 is an irrational