Square Root of 256
The square root of 256 is exactly 16. Yes, 256 is a perfect square. Its square root, 16, is a whole number.
Where √256 sits
256 is a perfect square: 16 × 16 = 256, so √256 is exactly 16. No estimating needed.
| k | k² | Compared to 256 |
|---|---|---|
| 14 | 196 | 60 below |
| 15 | 225 | 31 below |
| 16 | 256 | equal |
| 17 | 289 | 33 above |
| 18 | 324 | 68 above |
| 19 | 361 | 105 above |
Exact form from the prime factors
256 = 2^8. Every prime appears an even number of times, so the whole thing comes out of the square root: √256 = 16.
Frequently Asked Questions
What is the square root of 256?
The square root of 256 is exactly 16.
Is 256 a perfect square?
Yes, 256 is a perfect square. Its square root, 16, is a whole number.
What two whole numbers is √256 between?
None needed -- √256 is exactly 16, a whole number. For context, the perfect squares just before and after 256 are 225 (15²) and 289 (17²).
What are the square roots of the numbers right next to 256?
√255 is about 15.9687, and √257 is about 16.0312. 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 √256 squared?
Exactly 256 -- squaring undoes the square root. Squaring the rounded decimal 16 gives 256, which is why the radical form 16 is the exact answer and the decimal is an approximation.
What is the negative square root of 256?
−16. Every positive number has two square roots, one positive and one negative, because (−16)² is also 256. The radical sign √ by convention means the positive one.
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