Square Root of 121
The square root of 121 is exactly 11. Yes, 121 is a perfect square. Its square root, 11, is a whole number.
Where √121 sits
121 is a perfect square: 11 × 11 = 121, so √121 is exactly 11. No estimating needed.
| k | k² | Compared to 121 |
|---|---|---|
| 9 | 81 | 40 below |
| 10 | 100 | 21 below |
| 11 | 121 | equal |
| 12 | 144 | 23 above |
| 13 | 169 | 48 above |
| 14 | 196 | 75 above |
Exact form from the prime factors
121 = 11^2. Every prime appears an even number of times, so the whole thing comes out of the square root: √121 = 11.
Frequently Asked Questions
What is the square root of 121?
The square root of 121 is exactly 11.
Is 121 a perfect square?
Yes, 121 is a perfect square. Its square root, 11, is a whole number.
What two whole numbers is √121 between?
None needed -- √121 is exactly 11, a whole number. For context, the perfect squares just before and after 121 are 100 (10²) and 144 (12²).
What are the square roots of the numbers right next to 121?
√120 is about 10.9545, and √122 is about 11.0454. 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 √121 squared?
Exactly 121 -- squaring undoes the square root. Squaring the rounded decimal 11 gives 121, which is why the radical form 11 is the exact answer and the decimal is an approximation.
What is the negative square root of 121?
−11. Every positive number has two square roots, one positive and one negative, because (−11)² is also 121. The radical sign √ by convention means the positive one.
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