(Q6).Prove that the following are irrational.?

(i)
1
√2
Let us assume
1
√2
 is rational.

So we can write this number as.

1
√2
 =
a
b
 ........1

Here, a and b are two co-prime numbers and b is not equal to .

1 =
a√2
b

Now, divide by b, we get.

b = a√2 or
b
a
 = √2
Here, a and b are integers so,
a
b
 is a number.

so √2 should be a number

But this contradicts the fact that √2 is an number.

Therefore,
1
√2
 is number.