Square Root of 324
The square root of 324 is exactly 18. Yes, 324 is a perfect square. Its square root, 18, is a whole number.
Where √324 sits
324 is a perfect square: 18 × 18 = 324, so √324 is exactly 18. No estimating needed.
| k | k² | Compared to 324 |
|---|---|---|
| 16 | 256 | 68 below |
| 17 | 289 | 35 below |
| 18 | 324 | equal |
| 19 | 361 | 37 above |
| 20 | 400 | 76 above |
| 21 | 441 | 117 above |
Exact form from the prime factors
324 = 2^2 × 3^4. Every prime appears an even number of times, so the whole thing comes out of the square root: √324 = 18.
Frequently Asked Questions
What is the square root of 324?
The square root of 324 is exactly 18.
Is 324 a perfect square?
Yes, 324 is a perfect square. Its square root, 18, is a whole number.
What two whole numbers is √324 between?
None needed -- √324 is exactly 18, a whole number. For context, the perfect squares just before and after 324 are 289 (17²) and 361 (19²).
What are the square roots of the numbers right next to 324?
√323 is about 17.9722, and √325 is about 18.0278. 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 √324 squared?
Exactly 324 -- squaring undoes the square root. Squaring the rounded decimal 18 gives 324, which is why the radical form 18 is the exact answer and the decimal is an approximation.
What is the negative square root of 324?
−18. Every positive number has two square roots, one positive and one negative, because (−18)² is also 324. The radical sign √ by convention means the positive one.
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