Can we add root 2 and root 2?

Can You Add √2 and √2?

Yes, you absolutely can add √2 and √2 — and the result might be simpler than you think. While it’s true that, in general, you can’t combine unlike radical terms (just like you can’t add apples and oranges), √2 and √2 are like terms. That means they have the same radical part, so they can be combined.

Think of it this way: if you have one √2 and add another √2, you end up with two of them. Mathematically, that’s:

√2 + √2 = 2√2

This is no different from saying x + x = 2x — it’s just that our "x" happens to be an irrational number, √2. You’re not simplifying √2 itself (since it’s approximately 1.414 and goes on forever), but you are simplifying the expression by combining like terms.

It’s important to remember that this rule only works when the radicals are identical. For example, you can’t simplify √2 + √3 in the same way because they’re different radicals — those are the “apples and oranges” scenario. But when the roots match, addition is straightforward.

So, far from being a tricky exception, adding √2 + √2 is a great example of how consistent the rules of algebra are — even when dealing with irrational numbers. The key is recognizing like terms and knowing when (and when not) to combine them.