Question

14. Prove that rootp + rootq is irrational, where p, q are primes.
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Answer 1

Answer:

Step-by-step explanation:

Let √p+√q be a rational number.

:- √p+√q=a/b , where a and b are co primes and b is not equal.to zero.

Squaring both the sides.

p^2 +q^2 +2√pq=a^2 /b^2

2√pq =a^2/b^2 -p^2-q^2

√pq=a^2-p^2b^2-q^2b^2/2b^2

Now √pq is irrational and r.h.s side is rational.

So their equality is not possible .

Therefore, our supposition is wrong.

Hence, √p+√q is irrational.proved.