Question

prove that ✓5 is irrational​

Answer 1

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Answer 2

Step-by-step explanation:

Let us assume √5 is rational ,then every rational number is of the form p/q ( where p and q are co-primes)

So, √ 5 = p/q

SQUARING ON BOTH SIDES ,we get

5² =( p/q)²

If we transpose q² to left side ,we get

( 5q)² = p²

Let p= 5s then

SQUARING ON BOTH SIDES ,we get

(5q² )²= (5s)²

25q²= 5s²

5q² = s²

If s² is a multiple of 5 then s is also a multiple of 5

But this contradicts the fact that p and q are co-primes

Therefore , √ 5 is irrational