Question

is i
3. Pove that the following
are irrational
(1) 1/root2​

Answer 1

Step-by-step explanation:

b/a = rational number

1/root 2= irrational number

hence rational number and irrational is not equal

so, it is proved

Answer 2

Step-by-step explanation:

Let us assume, to the contrary, that 1/root2 is rational.

That is, we can find coprime a and b (b is not equal to zero)

1/root2=a/b

therefore 1=root2×a÷b

since a and b are integers, we get root2×a÷b is rational, and so 1 is rational.

but this contradicts the fact that 1 is irraitonal.

but this contradiction has arisen because of our incorrect assumption that 1/root2 is rational