Question

If p,q arepositive integers,prove √[p]+√[q] is irrational

Answer 1

Heya !!

Here's your answer.. ⬇

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➡ Given :- p and q are positive prime integers.

➡ To Prove :- √p + √q is an irrational no.

➡ Proof :- Let √p + √q = a/b is a rational no.

√p = a/b - √q

Take square on both side..

( √p )² = ( a/b - √q )²

p = (a/b)² - 2a/b × √q + q

p - (a/b)² - q = - 2a/b × √q

( p - (a/b)² - q ) × b/2a = √q

rational ≠ irrational.

q is positive prime integer and root of prime no. is irrational no.

Hence, √p + √q is an irrational no.

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Hope it helps..

Thanks :)