for 7√27 I think you have to see what can come out off the 27
√27
∧
9 3
∧
3 3
A 3 comes out because there is two and the other 3 stays in, so your left with
3·7√3 = 21√3
for 5√48 Two 2s come out and a 3 stays in so, it looks like 4·5√3= 20√3
and than just add
I hope this looks familiar.