Question

prove that
$\sqrt{5}$
is irrational​

Answer 1

Answer:

Step-by-step explanation:

Let √5 be a rational number.

then it must be in form of p/q

where, qnot equal to 0 ( p and q are co-prime)

√5=p/q

√5×q=p

Suaring on both sides,

5q^2=p^2 ----------------(I)

P^2 is divisible by 5

p = 5C

Suaring on both sides,

P^2=25c^2 --------------(ii)

Put p^2 in equation (i)

5q^2=25(c) ^2

q^2=5c^2

So, q is divisible by 5.

So, there is a contradiction as per our assumption.

We have assumed p and q are co-prime but here they a common factor of 5.

The above statement contradicts our assumption.

Therefore, √5 is an irrational number.

#its Sayan.