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prove that 2 upon under root 7 is irrational number

Posted by Priya Yadav 3 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Ansh Pandey 3 years, 6 months ago

First assume 2/root7 is rational So,2/root 7=a/b ( a and are coprime number Square both side, we get, 4/7=a²/b² 4b²/7=a² So 4/7 is factor of a² So 4/7 is also factor of a (by theorem) Now let a=4/7c ( for any integer c) so we get, (4/7c)²=4b²/7 16/49c²=4b²/7 b²=4/7c² So 4/7 is factor of b² So 4/7 is also factor of b So a and b are not coprime So our assumption is wrong So 2/root7 is irrational number (This is proved by contradiction method)

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CBSE > Class 10 > Mathematics