Question

Prove that root 7 is irrational

Answer 1

To prove 2/root 7 is irrational, you have to show that root 7 is irrational, as you know that when a rational number is divided by irrational no. then the no. obtained is irrational. We can do this by method of contradiction. =>root 7 =p/q, where p and q are coprimes and q is not equal to 0.

Answer 2

To prove 2/root 7 is irrational, you have to show that root 7 is irrational, as you know that when a rational number is divided by irrational no. then the no. obtained is irrational.

To prove- Root 7 is irrational.

Proof-

We can do this by method of contradiction.

Let root 7 is rational.

=> root 7 =p/q, where p and q are coprimes and q is not equal to 0.

=> 7=(p^2)/(q^2)

=>p^2= 7q^2

=>7 is factor of p^2

=> 7 is factor of p

=>p=7k, where k is a constant

=>p^2=49k^2

=>7q^2=49k^2

=>q^2=7k^2

=> 7 is also a factor of q^2 and thus a factor of q.

p and q have 7 as a common factor except 1.

This is a pure contradiction to the fact that p and q are coprimes i.e they have only 1 as the common factor.

So our assumption that root 7 was rational is wrong.

Root 7 is irrational.

So 2, a rational no. When divided by root 7 the answer is irrational.