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Prove that root5 is irrational

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Prove that root5 is irrational

Posted by Kamboj Kamboj 7 years, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Anjali Pokhariya 7 years, 3 months ago

Let root5 is a rational number where root5=a/b and b is not = 0 Then root5 =a/b Squaring both side 5=a×a/b×b 5bsquare=a square a is divisible by 5 5 is a factor of a Let 5c=a Then 5bsquare =(5c)square 5bsquare =25csquare bsquare = 5csquare Then bsquare is a factor of 5 b is also a factor of 5 Hence,a and b are co prime numbers Therefore,our contradict the fact that root5 is an irrational number Hence,our supposition is wrong Therefore, root5 is an irrational number Hence Proved

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CBSE > Class 10 > Mathematics