Question

1. Prove that V5 is irrational.​

Answer 1

Answer:

sory

Step-by-step explanation:

Answer 2

Answer:

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)

v5=p/q

5×q=p

Suaring on both sides,

5q² =p² --------------(1)

p² is divisible by 5.

So, p is divisible by 5.

p=5c

Suaring on both sides

p² =25c² --------------(2)

Put p² in eqn.(1)

5q²=25(c)²

q² =5c²

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,

v5 is an irrational number.