Question

prove that under root 2 + under root Q is irrational where p and q are prime.if knows then only answer.plz

Answer 1

Hey !!

Here is your answer.. ⬇⬇⬇

To Prove :- √p + √q is irrational number. Where P and q are primes.

Proff :- let √p + √q = x is a rational number.

√p = x - √q

Taking Square On Both The Side.. We Get...,,

${( \sqrt{p}) }^{2} = {(x - \sqrt{q}) }^{2} \\ \\ p = {x}^{2} - 2x \sqrt{q} + q \\ \\ 2x \sqrt{q} = {x}^{2} + q - p \\ \\ \sqrt{q} = \frac{ {x}^{2} + q - p }{2x}$


Here it is contradiction..

R.H.S is rational while L.H.S I irritational.

Hence, √p + √q I irrational number. .... ( proved )


HOPE IT HELPS YOU....

THANKS ^-^