Can I write √ 1 as 1?

Is √1 the Same as 1?

Yes, you can write √1 as 1—and in fact, that’s exactly what it is. The square root of 1 equals 1 because 1 multiplied by itself gives you 1. While every positive number technically has both a positive and negative square root (since both 1 × 1 and (–1) × (–1) equal 1), the symbol √ refers specifically to the principal (positive) square root. So when you see √1, it’s understood to mean the positive value: 1.

This might seem trivial, but it’s an important detail in mathematics. The convention of taking the positive root ensures consistency, especially in geometry, physics, and engineering, where negative lengths or values don’t make sense. For example, if you’re calculating the length of a side of a square with area 1, you wouldn’t say it’s –1 units long. You’d say it’s 1—simple and straightforward.

Still, it’s worth remembering that while √1 = 1, the equation x² = 1 has two solutions: x = 1 and x = –1. The square root symbol itself, however, only gives you the principal (positive) one. So yes, √1 is 1—but the full story has a little nuance.