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Prove that root 6 + root 5 is irrational number |
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Answer» This question can be SOLVED in two ways. 1)Let us assume, to the CONTRARY, that √5+√6 is irrational. So we can find two integers numbers a and b(≠0), in the FOLLOWING way, √5+√6 = a/bRearranging, √5 = a/b - √6= integer/integer - RATIONAL ...( as √6 is assume as rational)So, this means that √5 is rational. But this contradict the fact that √5 is irrational. Our assumption is wrong. Hence, √5 + √6 is irrational. 2) Let us assume, to the contrary, that √5+√6 is irrational. So we can find two integers numbers a and b(≠0), in the following way, √5+√6 = a/bRearranging, √6 = a/b - √5= integer/integer - rational ...( as √5 is assume as rational)So, this means that √6 is rational. But this contradict the fact that √6 is irrational. Our assumption is wrong. Hence, √5 + √6 is irrational. Hope it may help you!!!! |
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