Square Root of 361
The square root of 361 is exactly 19. Yes, 361 is a perfect square. Its square root, 19, is a whole number.
Where √361 sits
361 is a perfect square: 19 × 19 = 361, so √361 is exactly 19. No estimating needed.
| k | k² | Compared to 361 |
|---|---|---|
| 17 | 289 | 72 below |
| 18 | 324 | 37 below |
| 19 | 361 | equal |
| 20 | 400 | 39 above |
| 21 | 441 | 80 above |
| 22 | 484 | 123 above |
Exact form from the prime factors
361 = 19^2. Every prime appears an even number of times, so the whole thing comes out of the square root: √361 = 19.
Frequently Asked Questions
What is the square root of 361?
The square root of 361 is exactly 19.
Is 361 a perfect square?
Yes, 361 is a perfect square. Its square root, 19, is a whole number.
What two whole numbers is √361 between?
None needed -- √361 is exactly 19, a whole number. For context, the perfect squares just before and after 361 are 324 (18²) and 400 (20²).
What are the square roots of the numbers right next to 361?
√360 is about 18.9737, and √362 is about 19.0263. 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 √361 squared?
Exactly 361 -- squaring undoes the square root. Squaring the rounded decimal 19 gives 361, which is why the radical form 19 is the exact answer and the decimal is an approximation.
What is the negative square root of 361?
−19. Every positive number has two square roots, one positive and one negative, because (−19)² is also 361. The radical sign √ by convention means the positive one.
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