Question

Why are these incorrect 3sqrt 7 - sqrt 7 =3

Answer 1

Because the left side sqrt is multiplied by 3 if it was just added it would be correct because it would cancel out and leave the 3’s. Since it’s multiplied it would change the value

Answer 2

$\bf 3\sqrt{7}-\sqrt{7}=3\implies 3\sqrt{7}-1\sqrt{7}=3\implies \stackrel{\textit{adding like-terms}}{2\sqrt{7}\ne 3}$

bear in mind that 3√7, is really 1√7 + 1√7 + 1√7, if we subtract 1√7 from it, we're left with 2√7.