Question

prove that 2+3underroot 5 is irrational

Answer 1

•let us assume to the opposite i.e,
2-3√5 as rational .

•°•Therefore ,2-3√5 can be written in the form of a/b.

where a and b are co-prime numbers.

→2-3√5=a/b 

→ -3√5=a/b-2

→ -3√5= a-2b/b

→ -√5=a-2b/3

•Where -√5 is an irrational number and a-2b/3 is a rational number.

Hence √5 is irrational.

This is a contradiction
i.e Rational≠Irrational.

Hence it is an irrational number.

Thank you!☺️