Question

prove that 5+ under root 5 is an irrational number. ​

Answer 1

Step-by-step explanation:

Let 5 be a rational number.

then it must be in form of qp

where, q=0 ( p and q are co-prime)

5 = qp

5 ×q=p

Suaring on both sides,

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

p ^2 is divisible by 5.

So, p is divisible by 5.

p=5c

Suaring 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.