How to represent root 1?

Understanding the Square Root of 1

When you see the symbol √1, you're looking at the principal square root of 1 — and that’s simply 1. It might seem straightforward, but there's a subtle mathematical idea at play here. While both 1 and −1 are square roots of 1 (since 1² = 1 and (−1)² = 1), the radical symbol √ always refers to the non-negative, or principal, root.

This convention helps avoid confusion in calculations and ensures consistency across mathematics. So even though 1 has two square roots, √1 unambiguously equals 1. This rule applies to all square roots: whether you're dealing with √4, √9, or √1, the symbol points to the positive solution by default.

It’s a small detail, but an important one — especially when solving equations or working with functions where sign matters. For instance, in geometry or physics, taking the negative root might not make sense (you can’t have a negative length), so the principal root keeps things grounded in reality.

In everyday math, when someone asks for “the square root” of 1, they’re usually expecting 1 — and thanks to the definition of the principal root, that’s exactly what √1 gives you. The existence of −1 as another root is still valid, but it’s expressed only when explicitly needed, such as when solving quadratic equations where both solutions must be considered.

So, while the math behind it has depth, the answer is simple: √1 = 1, by definition and design.