Question

prove that root 7 is irrational

Answer 1

root 7= 2.645751311
which cannot be written in p/q form and cannot be terminate nor repeating so it is a irrational number

Answer 2

Step-by-step explanation:

Let us assume that √7 is a rational no.

∴ √7= p/q, q≠0, p and q are co-primes.

Squaring on both sides,

(√7)² = p²/q²

7 = p²/q²

7q² = p²           ...(eq.1)

q²= p²/7           ...(p² is divisible by 7 ⇒ p is also divisible by 7)

Let p=7c           ...(substitute p=7c in eq.1)

7q²=(7c)²

7q²=49c²

q²=7c²

c²=q²/7             ...(q² is divisible by 7⇒ q is divisible by 7)

∴7 divides both p and q. This contradicts the assumption that both p and q have no common factor other than 1. This contradiction has occured because of our incorrect assumption, that √7 is a rational no.. Hence, √7 is an irrational no.

Hope helped!!