prove that 3+2√5 is irrtatonal
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we know that root 5 is irrational so product of a rational number and irrational number is irrational number that is 2 root 5 is irrational number now 3 + 2 root 5 that is three plus in rational number but 3 is a rational number hence we conclude that the sum of a rational number and irrational number is always a irrational number hence it is prove that 3 + 2 root 5 is irrational number
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Step-by-step explanation:
Solving3 + 2√5 = a/b we get,
=>2√5 = a/b – 3
=>2√5 = (a-3b)/b
=>√5 = (a-3b)/2b
This 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 number
Hence proved.
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