Hello, rj2001!

I understand . . . These are all fourth roots.

. . I'll drop all the indexes (the 4's).

^4√(6a^9) + ^4√(3750a) - ^4√(6a)

The first radical is: .√(6a·a^8) .= .√(a^8)·√(6a) .= .a²·√(6a)

The second is: .√(625·6a) .= .√(625)·√(6a) .= .5·√(6a)

And we have: .a²·√(6a) + 5·√(6a) - √(6a) . = . a²·√(6a) + 4·√(6a)

. . . . . = . (a² + 4)·√(6a)

Now you can insert the "4" . . .