Question

prove that (2√3+√5)is an irrational number also check whether (2√3+√5) (2√3-√5 is rational or irrational

Answer 1

2 ROOT 3 AND ROOT 5 ARE IRRATIONAL NUMBERS.SO WHEN ADDED THEY GIVE US AN IRRATIONAL NUMBER.
(2 ROOT 3 +ROOT 5)(2 ROOT 3- ROOT 5) IS RATIONAL
BECAUSE
IDENTITY:(a+b)(a-b)=a^2-b^2
SO
(2 ROOT 3)^2 -(ROOT 5)^2
12-5
7
7 IS A RATIONAL NUMBER 
HENCE PROVED