Question

prove that 7√5 is irrational​

Answer 1

Yes it is a irrational number because it cannot be converted in rational number

Answer 2

On the contrary let us suppose that √5 is rational in 7√5.

So √5 can be written in the form of p/q where p and q are integers and q is not equal to 0.

So, √5 = p/q

or 5 = p^2/q^2...................1

or p^2 = 5 q^2.

Therefore 5 is a factor of p^2, so it divides p also.

and, 5 k = p.

Now, from........... 1,

5 = 25k^2/q.

Therefore q^2=5k^2.

Therefore 5 is so factor of q^2. so, it divides q also.

But, this contradicts are assumption. Therefore our assumption was wrong √5 is an irrational no.

therefore , 7√5 is and irrational number.