Square Root of 1
The square root of 1 is exactly 1. Yes, 1 is a perfect square. Its square root, 1, is a whole number.
Where √1 sits
1 is a perfect square: 1 × 1 = 1, so √1 is exactly 1. No estimating needed.
| k | k² | Compared to 1 |
|---|---|---|
| 1 | 1 | equal |
| 2 | 4 | 3 above |
| 3 | 9 | 8 above |
| 4 | 16 | 15 above |
| 5 | 25 | 24 above |
| 6 | 36 | 35 above |
Exact form from the prime factors
1 = n/a. Every prime appears an even number of times, so the whole thing comes out of the square root: √1 = 1.
Frequently Asked Questions
What is the square root of 1?
The square root of 1 is exactly 1.
Is 1 a perfect square?
Yes, 1 is a perfect square. Its square root, 1, is a whole number.
What two whole numbers is √1 between?
None needed -- √1 is exactly 1, a whole number. For context, the perfect squares just before and after 1 are 0 (0²) and 4 (2²).
What are the square roots of the numbers right next to 1?
√0 is exactly 0, and √2 is about 1.4142. Square roots increase more slowly as the number gets bigger, which is why consecutive whole numbers have roots that get closer together the higher you go.
What is √1 squared?
Exactly 1 -- squaring undoes the square root. Squaring the rounded decimal 1 gives 1, which is why the radical form 1 is the exact answer and the decimal is an approximation.
What is the negative square root of 1?
−1. Every positive number has two square roots, one positive and one negative, because (−1)² is also 1. The radical sign √ by convention means the positive one.
More Number Theory
- Square Root Calculator (look up any number)
- Factors of 1
- GCF Calculator
- LCM Calculator