Square Root of 144
The square root of 144 is exactly 12. Yes, 144 is a perfect square. Its square root, 12, is a whole number.
Where √144 sits
144 is a perfect square: 12 × 12 = 144, so √144 is exactly 12. No estimating needed.
| k | k² | Compared to 144 |
|---|---|---|
| 10 | 100 | 44 below |
| 11 | 121 | 23 below |
| 12 | 144 | equal |
| 13 | 169 | 25 above |
| 14 | 196 | 52 above |
| 15 | 225 | 81 above |
Exact form from the prime factors
144 = 2^4 × 3^2. Every prime appears an even number of times, so the whole thing comes out of the square root: √144 = 12.
Frequently Asked Questions
What is the square root of 144?
The square root of 144 is exactly 12.
Is 144 a perfect square?
Yes, 144 is a perfect square. Its square root, 12, is a whole number.
What two whole numbers is √144 between?
None needed -- √144 is exactly 12, a whole number. For context, the perfect squares just before and after 144 are 121 (11²) and 169 (13²).
What are the square roots of the numbers right next to 144?
√143 is about 11.9583, and √145 is about 12.0416. 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 √144 squared?
Exactly 144 -- squaring undoes the square root. Squaring the rounded decimal 12 gives 144, which is why the radical form 12 is the exact answer and the decimal is an approximation.
What is the negative square root of 144?
−12. Every positive number has two square roots, one positive and one negative, because (−12)² is also 144. The radical sign √ by convention means the positive one.
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