Question

Prove that the following are irrationals:
(i) 1/√2
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Answer 1

Step-by-step explanation:

1\√2

1=1

√2=1.414....

therefore, 1\1.414.....

so it is not an irrational number

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Answer 2

: Solution

➝ 1/√2 is rational.

➢Then we can find co-prime x and y (y ≠ 0) such that 1/√2 = x/y

➝ Rearranging, we get,

➢√2 = y/x

➢Since, x and y are integers, thus, √2 is a rational number, which contradicts the fact that √2 is irrational.

➢ Hence, we can conclude that 1/√2 is irrational.