prove that √5 is an irrational number
hey guys help me
Don’t spam​

2 thoughts on “prove that √5 is an irrational number<br />hey guys help me <br />Don’t spam​”

1. Answer:

   Let us assume the opposite, i.e., √5 is a rational number. Hence, √5 can be written as in the form ab where a and b(b≠0) are co-prime (no common factor other than 1 ). By theorem: if p is a prime number and p divides a2, then p divides a, where a in a positive number.

   Reply

2. Answer:

   I HOPE THIS MAY HELP YOU ITS EASY❤❤❤

   Step-by-step explanation:

   Given: √5

   We need to prove that √5 is irrational

   Proof:

   Let us assume that √5 is a rational number.

   So it 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 number.

   Hence proved

   Reply