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Prove that 3+2 √5 is irrational

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Prove that 3+2 √5 is irrational

Posted by Aashutosh Upadhyay 6 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Chirag Jain 6 years, 10 months ago

Let us assume 3+√5 is a rational number But all the rational no. are in the form p/q So we can also write 3+√5 in p/q form and when we divide p/q with any of their common factor we get a/b which are coprime 3+√5 = a/b √5 = a/b-3 √5= a-3b/b But we know a-3b/b is a rational no But √5 is an irrational number => Our assumption is wrong. => 3+√5 is an irrational no

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