Question

27. Prove that √2 + √3 is irrational​

Answer 1

Solution: Please reference to image attached to answer.

Explanation:

1. Let √2 + √3 be a rational number a/b (say).

2. Square both sides of equation

3. Solve equation and u will get value of √6 in rational form i.e., p/q

4. This contradict fact that √6 is irrational & can't be in p/q form.

5. Hence √2 + √3 can't also be rational number.

Hence Proved

Answer 2

Answer:

Let √2 + √3 be a rational number a/b (say).

2. Square both sides of equation

3. Solve equation and u will get value of √6 in rational form i.e., p/q

4. This contradict fact that √6 is irrational & can't be in p/q form.

5. Hence √2 + √3 can't also be rational number.

Hence Proved

Step-by-step explanation: