Square Root of 9
The square root of 9 is exactly 3. Yes, 9 is a perfect square. Its square root, 3, is a whole number.
Where √9 sits
9 is a perfect square: 3 × 3 = 9, so √9 is exactly 3. No estimating needed.
| k | k² | Compared to 9 |
|---|---|---|
| 1 | 1 | 8 below |
| 2 | 4 | 5 below |
| 3 | 9 | equal |
| 4 | 16 | 7 above |
| 5 | 25 | 16 above |
| 6 | 36 | 27 above |
Exact form from the prime factors
9 = 3^2. Every prime appears an even number of times, so the whole thing comes out of the square root: √9 = 3.
Frequently Asked Questions
What is the square root of 9?
The square root of 9 is exactly 3.
Is 9 a perfect square?
Yes, 9 is a perfect square. Its square root, 3, is a whole number.
What two whole numbers is √9 between?
None needed -- √9 is exactly 3, a whole number. For context, the perfect squares just before and after 9 are 4 (2²) and 16 (4²).
What are the square roots of the numbers right next to 9?
√8 is about 2.8284, and √10 is about 3.1623. 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 √9 squared?
Exactly 9 -- squaring undoes the square root. Squaring the rounded decimal 3 gives 9, which is why the radical form 3 is the exact answer and the decimal is an approximation.
What is the negative square root of 9?
−3. Every positive number has two square roots, one positive and one negative, because (−3)² is also 9. The radical sign √ by convention means the positive one.
More Number Theory
- Square Root Calculator (look up any number)
- Factors of 9
- GCF Calculator
- LCM Calculator