Question says about what number can you add to
[tex]\sqrt{7}[/tex] to get a rational number.
We know that rational numbers are the numbers which are written in form of p/q where p and q both are integers.
but q can never be 0.
If we add only some integer or real number to [tex]\sqrt{7}[/tex] then we will still get irrational number which is not of the form p/q.
so the only way to finish the radical part is to use the opposite of that [tex]\sqrt{7}[/tex] which is -[tex]\sqrt{7}[/tex]
As you can see that
[tex]\sqrt{7}[/tex] - [tex]\sqrt{7}[/tex] = 0
and we know that 0 is a rational number because that can be written as 0/1 in p/q form.
Hence final answer is -[tex]\sqrt{7}[/tex]
