Question

Prove that (√3 + √5 ) is irrational.

Answer 1

Do it this way...
First prove either √3 or √5 as irrational then add the statement that any no. if added to an irrational no. is irrational....
i.e. If √3 is irrational.....then √3+√5 will also be irrational......( irr. no. + any no. = irr. no.)

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Answer 2

let's do 3 + root 5 irrational number therefore root 3 + root 5 is of the form P by q where p and q are integers and also p and q are coprime s

therefore do 3 is equals to 3 minus Root over 5 upon q
now lhs is root 3 which is a irrational number and RHS is p minus root 5 upon Q which is a rational number as we have assumed P upon Q to be a rational number

this is a contradiction as lhs is not equals to RSS therefore root 3 + root 5 is not a rational number and hence it is an irrational number