1.

If a is a non-zerorational and root bis a rational then showthat a/root b is a irrational​

Answer»

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.


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