Question

Probe that root 3 × root 5 is irrational

Answer 1

Answer:

Let √3.√5 be rational.

√3.√5=a/b (a,b are co primes, integers)

Squaring,

{√3.√5}^2=(a/b)^2

(√15)^2=a^2/b^2

15=a^2/b^2

15=(a/b)^2

√15=a/b

But we know that √15 is irrational. But RHS is rationol.

Therefore our assumption is contradicted.

So,√3.√5 is irrational.