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Hence is not a rational number, it is irrational.

2. Prove that 3+2 is irrational

Answer

Let take that 3+2 is a rational number.

So we can write this number as

3+2 =a/b

Here a and b are two co prime number and b is not equal to 0

Subtract 3 both side we get

2 = a/b -3

2 = (a-3b)/b

Now divide by 2, we get

= (a-3b)/2b

3. Prove that the following are irrationals:

(i) 1

(ii) 7

(iii) 6+

Answer

(i) Let take that 1

is a rational number.

So we can write this number as

=a/b

Here a and b are two co prime number and b is not equal to 0

Multiply by

both sides we get

1=(a

)/b

Now multiply by b

b=a

divide by a we get