Question

prove that 7 is an irrational
number
Hence show that .
5+2 7 is also an irrational
munber

Answer 1

Step-by-step explanation:

Let us assume that root 7 is rational number and it is written in the form of p/q where p and q are Co prime integer....

Root 7=p/q

Root 7 x q = p

Square on both sides

7q ^2=p^2-----------------(1)

q^2=p^2/7

By theorem if p^2 is divisible by 7 so it is also divisible byp

So 7 is one of the multiple of p

P= 7 c

From eq 1

7q ^2=49 p 2

q^2=49p^2/7

q^2=7p^2

P^2=q^2/7

Again q is also divisible by 7

So our assumption is wrong p and q have common factor other than 1 it means p and q are not co prime so.. Root 7 is also an irrational number...