Show that 3√2 is not a irrational

1.	Show that 3√2 is not a irrational
Answer» Let us assume, to the contrary, that\xa03\xa0√\xa02\u200b\xa0is\xa0rational. Then, there exist co-prime positive integers\xa0a\xa0and\xa0b\xa0such that3\xa0√\xa02\u200b= a/b⇒ √\xa02 \u200b= a/3b\xa0⇒ √\xa02\u200b\xa0is rational ...[∵3,a\xa0and\xa0b\xa0are integers∴ 1/3b \u200bis a rational number]This contradicts the fact that √\xa02\u200b\xa0is irrational.\xa0So, our assumption is not correct.Hence,\xa03\xa0√\xa02\u200b\xa0is an irrational number.

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