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Prove that 3+2root5 is irrational |
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Answer» Letus assume that 3 + 2√5 is a rational number.Soit can be written in the form a/b3 + 2√5 = a/bHere a and b are coprime numbers and b ≠ 0Solving3 + 2√5 = a/b we get,=>2√5 = a/b – 3=>2√5 = (a-3b)/b=>√5 = (a-3b)/2bThis shows (a-3b)/2b is a rational number. But we know that But √5 is an irrational number.so it contradictsour assumption.Our assumption of3 + 2√5 is a rational number is incorrect.3 + 2√5 is an irrational numberHence proved Our Assumation is wrong, it\'s irrational numbers. |
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