Question

Prove that √3+√4 ia an irrational number

Answer 1

Answer

Step-by-step explanation:

1. Here 3^½+ 4^½= 3½+2

2. Let us assume that 3½+2 is a rational number

Then 3^½ +2= p/q, where q is not equal to zero.

3. By squaring both side, we have

3+4.3^½+4=p²/q²

7+4.3½=p²/q²

4.3½=p²/q² - 7

3^½= ( p²/q² - 7 ) ÷4

4. From the above equation it is evident that

LSH is an irrational number while RHS ia a

rational number which is not possible.

So we conclude that our assumption is

wrong from the start.

Hence 3^½+4^½ is an irrational number.