Question

show that root3 +2root5 is irrational

Answer 1

let us take 3+2√3 is a rational
=> 3+2√3 = p/q (where q is not equal to 0 and p and q are co prime numbers)
2√3= p/q-3
2√3= p-3q/q
√3=(p-3q/q)/2
√3=(p-3q/2q) which is a integer
but is we we know √3 is an irrational
3+2√3  is a irrational

Answer 2

heya...


let root3 + 2√5 is rational...
therefore they can be written in the form of
p/q..

here √3+2√5 = a/b..

where a;b are co-primes

now √3 +√5 = a/2b

= √3 + √5 = a/2b

but we know that a rational number is not equal to a irrational number..

this contradiction arised due to our incorrect assumption

therefore √3+2√5 is irrational...