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How to prove that √6 is …

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How to prove that √6 is irrational no

Posted by Kashish Matta 8 years, 7 months ago

CBSE > Class 09 > Mathematics

1 answers

Sukdeb Mukherjee 8 years, 7 months ago

let root 6 be rational no.

root 6 = a/b where a and b are integers , b not equal to zero and also a and b are coprime

6 = a²/b² (squaring both sides )

6b² = a²

b² = a²/6

therefore 6 is a factor of a ( 6 divides a²

so 6 divides a )

let us take a= 6c

now 6b²= a²

6b² = (6c)² (putting value of a )

6b² = 36c²

c² = 6b²/36

c² = b²/6

therefore 6 is also a factor of b ( 6 divides b²

so 6 divides b )

so 6 is a factor of a as well as b .this contradicts the fact that a and b are coprime . this is due to our assumption

that root 6 is rational

THEREFORE ROOT 6 IS IRRATIONAL

1Thank You

ANSWER

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