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Prove that 1/ root 2 is …

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Prove that 1/ root 2 is irrational

Posted by Shanmuga Lakshmi 1 year, 9 months ago

CBSE > Class 10 > Mathematics

1 answers

K. Hema 1 year, 9 months ago

Rationalize factor =root 2 =1/root 2×root 2/root 2 =Root 2/2 =root 2/2 is a rational number. Let us assume that root 2/2 is a rational number. root 2/2=p/q, q is not equal to 0 Where p and q are co-prime number. root 2/2=p/q Root 2=p/q×2 Multiplication of two rational number is a rational number. Thus root 2 is a rational number. But this contradicts the fact that root 2 is a irrational number. This contradiction arises because of our incorrect assumptions that 1/root 2 is a rational number. Hence 1/root 2 is a irrational number.

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