There is one asymmetry at the heart of this whole section, and everything else follows from it: multiplication passes through a radical sign, and addition does not. √2 · √3 really is √6, but √2 + √3 is not √5 — it is 3.146264, while √5 is only 2.236068. Adding radicals is therefore never about the numbers inside; it is about counting matching units, exactly like 5x + 2x. Step through each example one line at a time and watch which parts are allowed to move.
The picture
Every line equals—
Do these two combine?
FIRST2 – 200
SECOND2 – 200
Radical operations, one line at a timepick an operation, then an example