Question

Show that 7-root 5 is irrational, give that root 5is irrational.

Answer 1

$\mathfrak{Hey\:Dude!}$

$\mathfrak{Here's\:your\:answer:}$

Given that:

$\sqrt{5}$
Is an irrational number.

We need to prove that:

$7 \sqrt{5}$
Is an irrational number.

There's a property that whenever any irrational number is multiplied by any other irrational number, the resultant number is also an irrational number.

Therefore,

$7 \sqrt{5}$
Is also an irrational number.

$\textbf{Hence Proved!!}$

Answer 2

Let , 7-root5 is a rational no. is equals to r, where r is a rational no.
So,
7-root 5 = r
7-r = root 5.
Now,
LHS is a rational but RHS is an irrational.
So, our assumption was wrong; 7-root5 is not a rational no.
Therefore, 7-root5 is a irrational no.
Hence, proved.


Hope this will help you...☺☺