Question

root 2 is a rational number prove that 5 + 3 under root 2 is irrational

Answer 1

Hii friend!! assume that 5-2 root 3 is rational 5-2 root 3 = a/b , where a and b are integers .  -2 root 3 = a/b - 5 2 root 3 = 5 - ab  2 root 3 = 5b/b - a/b root 3 = 5b - a / 2b we know that a, b , 2 and 5 are integers and they are also rational  therefore root 3 will be rational  but we know that root 3 is irrational there is a contradiction so, 5 - 2 root 3 is an irrational number  hope u found it useful ^_^  

Answer 2

from above
5+3 under root 2 is irrational

Hope it helps you