Question

prove that ✓5 is an irrational​

Answer 1

Answer:

√5 is irrational

Step-by-step explanation:

Given: √5

We need to prove that V5 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 = p</q?

- 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 irrational number.

~~Hope it helpes !!!