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Prove that 1/√2 is irrational.

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Prove that 1/√2 is irrational.

Posted by Mayank Sharma 4 years, 7 months ago

CBSE > Class 10 > Mathematics

2 answers

Ranvijay Kumar 4 years, 7 months ago

Let us assume 21 is rational. So we can write this number as 21=ba ---- (1) Here, a and b are two co-prime numbers and b is not equal to zero. Simplify the equation (1) multiply by 2both sides, we get 1=ba2Now, divide by b, we get b=a2 or ab=2Here, a and b are integers so, ab is a rational number, so 2 should be a rational number. But 2 is a irrational number, so it is contradictory. Therefore, 21 is irrational number

Kashish Verma 4 years, 7 months ago

Let us assume 21 is rational. So we can write this number as 21=ba ---- (1) Here, a and b are two co-prime numbers and b is not equal to zero. Simplify the equation (1) multiply by 2both sides, we get 1=ba2 Now, divide by b, we get b=a2 or ab=2 Here, a and b are integers so, ab is a rational number, so 2 should be a rational number. But 2 is a irrational number, so it is contradictory. Therefore, 21 is irrational number

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