Question

prove 3√5+√2 is irrational​

Answer 1

Answer:

irrotational

Step-by-step explanation:

let 3+5√2 be rational and have only common factor 1. but it is not possible . It is contradiction to our assumption . so, 3+5√2 is a irrational.

Answer 2

Answer:

Let: Assume that 3√5+√2 is Rational.

As per the definition of a Rational number it is expressed in P/q form where q ≠ 0 and P,Q are Co-Primes.

∴  3√5+√2 is Rational and by the definition,

=> 3√5+√2 = p/q

= 3√5 = p - √2/q

= 3√5 = p - √2p/q

So, if p - √2p/q $p - \frac{\sqrt{2p} }{q}$ is Rational, 3√5 is also Rational whereas here it's not Possible.

∴ p and q are Co-Primes.

Hence, the Assumption that 3√5 + √2 is Rational has been proved False.

Hence Proved!