Square Root of 81
The square root of 81 is exactly 9. Yes, 81 is a perfect square. Its square root, 9, is a whole number.
Where √81 sits
81 is a perfect square: 9 × 9 = 81, so √81 is exactly 9. No estimating needed.
| k | k² | Compared to 81 |
|---|---|---|
| 7 | 49 | 32 below |
| 8 | 64 | 17 below |
| 9 | 81 | equal |
| 10 | 100 | 19 above |
| 11 | 121 | 40 above |
| 12 | 144 | 63 above |
Exact form from the prime factors
81 = 3^4. Every prime appears an even number of times, so the whole thing comes out of the square root: √81 = 9.
Frequently Asked Questions
What is the square root of 81?
The square root of 81 is exactly 9.
Is 81 a perfect square?
Yes, 81 is a perfect square. Its square root, 9, is a whole number.
What two whole numbers is √81 between?
None needed -- √81 is exactly 9, a whole number. For context, the perfect squares just before and after 81 are 64 (8²) and 100 (10²).
What are the square roots of the numbers right next to 81?
√80 is about 8.9443, and √82 is about 9.0554. 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 √81 squared?
Exactly 81 -- squaring undoes the square root. Squaring the rounded decimal 9 gives 81, which is why the radical form 9 is the exact answer and the decimal is an approximation.
What is the negative square root of 81?
−9. Every positive number has two square roots, one positive and one negative, because (−9)² is also 81. The radical sign √ by convention means the positive one.
More Number Theory
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