Prove that √p and √q is irrational if p and q are prime number

1.	Prove that √p and √q is irrational if p and q are prime number
Answer» Let us suppose that\xa0√p + √q\xa0is rational.\xa0Let\xa0√p + √q\xa0= a, where a is rational.\xa0=>\xa0√q\xa0= a –\xa0√p\xa0Squaring on both sides, we get\xa0q = a2\xa0+ p -\xa02a√p=>\xa0√p\xa0= (a2\xa0+ p - q)/2a, which is a contradiction as the right hand side is rational number, while√p\xa0is irrational.\xa0Hence,\xa0√p + √q\xa0is irrational.Read more on Brainly.in - https://brainly.in/question/2815918#readmore

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