Question

Prone
that V5 Irrational
3​

Answer 1

Let us assume the given number be rational and we will write the given number in p/q form

⇒5−

3

=

q

p

⇒

3

=

q

5q−p

We observe that LHS is irrational and RHS is rational, which is not possible.

This is contradiction.

Hence our assumption that given number is rational is false

⇒5−

3

is irrational

Answer 2

Answer:

Let us assume

√5 = rational

√5= a/b where a , b are co primes

√5b=a

Squaring on both sides

( √5b)²=a²

5b² = a².........equation 1

b²= a²/5

Here 5 divides a² , so it also divides a .

Now let a= 5c for some integer c.

Squaring on both sides.

a²= (5c)²

a²=25c²

15b²=25c² ( from equation1 )

b²= 5c²

b²/5=c²

5 divides b² , so it can also divide b.

It isn't possible because a,b are co primes.

Therefore, our assumption is wrong.

√5 is irrational.

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