Question

What number can you add to \sqrt{7} " align="absmiddle" class="latex-formula">
to get a rational number?

Answer 1

Question says about what number can you add to

$\sqrt{7}$ 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 $\sqrt{7}$ 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 $\sqrt{7}$ which is -$\sqrt{7}$

As you can see that

$\sqrt{7}$ - $\sqrt{7}$ = 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 -$\sqrt{7}$