Question

Prove that root of p + root of q
is an irrational ,where p,q are primes

Answer 1

Let us assume p+√q is a

rational.

p+√q = a/b

Where a,b are integers and

b ≠ 0 .

=> √q = a/b - p

=> √q = (a-bp)/p

Since , a,b are integers, (a-bp)/p . so, √q is rational.

But , it contradicts the fact that

√q is an irrational.

Therefore,

p+√q is an irrational.

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