This week in pre-calc 11 we learned how to subtract and add radicals
the first step is to simplify the radical like example $sqrt {4}$ would be 2
no matter if the radical is mixed or entire for radicand must be the same
Example: You can’t add $sqrt (2)$ and $sqrt (3)$
In this example I show how when the radicand is the same you can add them $sqrt (2)$ + $sqrt (2)$ = $sqrt (4)$ which equals 2

When the radicand is not the same you have to try to use prime factorization to give the radicand a coefficient which hopefully ends in a radical that has the same radicand

Radicals with coefficients add and subtract differently, in this example I show how to made entire radicals into mixed to give them coefficients to make the radicands equal and show that in subtracting and adding mixed radicals with the same radicand you add or subtract the coefficient.

Remember that radicals without a coefficient have a hidden coefficient of 1.