Question

1. Prove that V5 is irrational​

Answer 1

Step-by-step explanation:

Let root 5 be rational

then it must in form of p/q

(q is not equal to 0)

(p and q are Co prime)

root = 5 x q = p

square on both sides

= 5 x q x q = p x p -----> 1

p x p is divisible by 5

p is divisible by 5

p = 5c ( c is a positive integer )

( squaring on both sides)

p x p = 25 c x c ------> 2

sub p x p in 1

5 x q x q = 25 x c x c

q x q = 5 x c x c

= q is divisible by 5

thus q and p have a common factor 5

there is a contradiction

as our assumption p and q are Co prime, but it has common factor

So, √5 is an irrational number

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