Question

show that √5 is irrational​

Answer 1

Step-by-step explanation:

I hope it helps you....

Answer 2

Step-by-step explanation:

Let √5 be a rational number,

then it must be in form of p/q, where, q is not equal to 0 ( p and q are co-prime)

√5 = p/q

√5×q=p

Squaring on both sides,

5q^2 =p^2 --------------(1)

p ^2 is divisible by 5.

So, p is divisible by 5.

p=5c

Squaring on both sides,

p^2=25c^2 --------------(2)

Put p^2 in eqn.(1)

5q^2=25(c)^2

q^2=5c^2

So, q is divisible by 5.

Thus p and q have a common factor of 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.