Is 1 its own square root?

Is 1 Its Own Square Root?

Yes, 1 is its own square root—and not just in one way, but in a couple of interesting mathematical senses. When you multiply 1 by itself, you get 1 (since 1 × 1 = 1), which means it’s a perfect square and its square root is indeed itself.

But here’s where it gets slightly more nuanced: every positive number technically has two square roots—one positive and one negative. In the case of 1, both 1 and −1 satisfy the equation x² = 1. After all, (−1) × (−1) also equals 1. So mathematically, both are valid square roots.

However, when someone asks, “What is the square root of 1?” they’re usually referring to the principal square root. By convention, the principal square root is defined as the non-negative one. So while −1 is a legitimate square root of 1, the answer we typically give—the one used in most calculations and formulas—is the positive version: 1.

This distinction matters in everything from basic algebra to advanced engineering. It’s why calculators return “1” when you input √1, not “±1”—they’re programmed to give the principal (non-negative) root by default.

So yes, 1 is its own square root in the principal sense, and it’s also the positive counterpart to −1 in the full set of real square roots. It’s a small detail, but one that reflects the quiet elegance of mathematical conventions—rules that keep things consistent, clear, and surprisingly human.