Question

Give an example to show that sum of one rational and one irrational number
is rational

Answer 1

Let take an equation

2+√3

Here, 2 is a rational number and √3 is an irratinal number.

Now, suppose that √3 is a rational number.

√3 = p/q

Squaring on both side we get

(√3)^2 = (p/q) ^2

3 = p^2/q^2

3 q^2 = p^2

P^2 is a multiple of 3

Therefore 3 is also a multiple of 3.

P has a factor of 3.------------1

(q)^2 = p^2/3

q^2 is a multiple of 3.

Therefore q is also a multiple of 3.

q also has a factor of 3.---------2

Both p and q has a factor of 3. Except 1 therefore our consideration is wrong.

Hence it proves that √3 is an Irrational number.

If any rational number is added with Irrational number then it must be Irrational.

Hence 2+√3 is an Irrational number.

Hope its help u.