Saved Bookmarks
| 1. |
Prove that √5 is irrational number |
|
Answer» We need to prove that √5 is irrationalStep-by-step explanation:Sp it t can be expressed in the FORM p/q where p,q are co-prime integers and q≠0 ⇒√5=p/q On squaring both the SIDES we get, ⇒5=p²/q² ⇒5q²=p² —————–(i) p²/5= q² So 5 divides p p is a MULTIPLE of 5 ⇒p=5m ⇒p²=25m² ————-(ii) From EQUATIONS (i) and (ii), we get, 5q²=25m² ⇒q²=5m² ⇒q² is a multiple of 5 ⇒q is a multiple of 5 Hence, p,q have a common factor 5. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number √5 is an IRRATIONAL numberHence proved |
|