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prove irrational( 3+root 2)

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prove irrational( 3+root 2)

Posted by Sonam Kumari Paswan 5 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 5 years ago

Let 3+√2 is an rational number.. such that
3+√2 = a/b ,where a and b are integers and b is not equal to zero ..
therefore,
3 + √2 = a/b
√2 = a/b -3
√2 = (3b-a) /b
therefore, √2 = (3b - a)/b is rational as a, b and 3 are integers..
It means that √2 is rational....
But this contradicts the fact that √2 is irrational..

So, it concludes that 3+√2 is irrational..
hence proved.

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