Question

If a is a non-zero
rational and root b
is a rational then show
that a/root b is a irrational​

Answer 1

Answer:

given: a is a rational number andis irrational.

TPT: a*is an irrational number.

proof:

this we will show by the contradiction.

letis a rational number.

therefore it can be represented as ration of two co-prime numbers.

let=, where p and q are co-primes................(1)

a is a rational number. letwhere m and n are co-primes...........(2)

.............(3)

⇒ b divides, therefore b divides.

let

thus b divides, therefore b divides mq.

thus pn and mq has at least one common factor b.

but from the assumption (1) and (2) pn and mq are co-primes.

therefore our assumption is wrong.

and is an irrational number

PLS MARK BRAINLIEST.