Can we add √ 3 and √ 2?

Can You Add √2 and √3?

It’s a common question in algebra: can you add two different square roots, like √2 and √3? The short answer is yes—but not in the way you might think. You can’t simplify √2 + √3 into a single radical or a neat expression like √5. Instead, you just leave it as is: √2 + √3.

If you’re working on a real-world problem and need a decimal approximation, go ahead and estimate. √2 is about 1.414, and √3 is roughly 1.732. Add them together, and you get around 3.146. That’s useful for practical calculations, like measuring distances or estimating areas.

In algebra and higher math, approximations don’t always cut it. Teachers and mathematicians often want exact forms—so instead of rounding, you keep the radicals untouched. Think of it like adding apples and oranges: you can have one apple and one orange, but you can’t claim you have two of the same fruit. Similarly, √2 and √3 are different irrational numbers, and they don’t combine into a simpler radical.

This idea becomes especially important when solving equations, simplifying expressions, or proving identities. Mixing decimals with exact forms can lead to errors down the line. So while √2 + √3 ≈ 3.146 is technically correct for estimation, the true, exact value remains written as √2 + √3.

The takeaway? Yes, you can add them. But in the world of exact math, sometimes the most accurate answer is the one that looks the least simplified.