Square Root of 289
The square root of 289 is exactly 17. Yes, 289 is a perfect square. Its square root, 17, is a whole number.
Where √289 sits
289 is a perfect square: 17 × 17 = 289, so √289 is exactly 17. No estimating needed.
| k | k² | Compared to 289 |
|---|---|---|
| 15 | 225 | 64 below |
| 16 | 256 | 33 below |
| 17 | 289 | equal |
| 18 | 324 | 35 above |
| 19 | 361 | 72 above |
| 20 | 400 | 111 above |
Exact form from the prime factors
289 = 17^2. Every prime appears an even number of times, so the whole thing comes out of the square root: √289 = 17.
Frequently Asked Questions
What is the square root of 289?
The square root of 289 is exactly 17.
Is 289 a perfect square?
Yes, 289 is a perfect square. Its square root, 17, is a whole number.
What two whole numbers is √289 between?
None needed -- √289 is exactly 17, a whole number. For context, the perfect squares just before and after 289 are 256 (16²) and 324 (18²).
What are the square roots of the numbers right next to 289?
√288 is about 16.9706, and √290 is about 17.0294. 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 √289 squared?
Exactly 289 -- squaring undoes the square root. Squaring the rounded decimal 17 gives 289, which is why the radical form 17 is the exact answer and the decimal is an approximation.
What is the negative square root of 289?
−17. Every positive number has two square roots, one positive and one negative, because (−17)² is also 289. The radical sign √ by convention means the positive one.
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