Question

prove that √5 is an irrational number​

Answer 1

Step-by-step explanation:

Let√5 be a rational no

1. √5=p/q (where p and q are the co-prime )
2. On squaring both side
3. (√5)²=(p/q)²
4. 5=p²/q²
5. 5q²=p²
6. Here 5 divides p²
7. therefore 5 divides p ( equation 1 ).
8. Now Let p=5k
9. than equation (1) be comes
10. 5q²=(5k)²
11. 5q²=25k²
12. q²=5k²
13. Here 5 divides q²
14. therefore 5 divides q ( equation 2 )
15. From equation (1) and (2). We come to know that 5 is common factor of both p and q respectively but p and q are co-prime So we get a contradiction therefore,Our assumptions is wrong. Therefore √5 is an irrational number.