Question

How do I add and subtract radicals with no like terms

Answer 1

Most real number arithmetic is pretty vacuous

`\sqrt 2 + \sqrt 3 = √(2) + √(3)`

That's about as good a way as possible to write this particular real number. But it's far from the only way.

`(\sqrt 2 + \sqrt 3)^2 = √(2)^2 + 2\sqrt 2 \sqrt 3 + √(3)^2 = 5 + 2 \sqrt 6`

so

`\sqrt 2 + \sqrt 3 = √(5 + 2 \sqrt 6)`

Sometimes you can factor something out and you have a common radical:

`√(32) + √(128) = √(2^5) + √(2^7) = 4 √(2) + 8 √(2) = 12 √(2)`

But most of them are vacuous,

`3√(7) + 34 √(13) = 3√(7) + 34 √(13)`