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proove that 5 + 2√5 is irrational

Posted by Ronit Vinod 4 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Account Deleted 4 years, 7 months ago

Let 5+2√5 be a rational number = p/q Where p and q are coprime numbers & q≠0 So 5+2√5 = p/q 2√5 = (p-5q)/q => √5 = (p-5q)/(2q) Since RHS is a rational number => √5 is a rational number But it contradicts the fact i.e.√5 is irrational number Therefore our assumption was incorrect => 5+2√5 is an irrational number Hence proved

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CBSE > Class 10 > Mathematics