Square Root of 225
The square root of 225 is exactly 15. Yes, 225 is a perfect square. Its square root, 15, is a whole number.
Where √225 sits
225 is a perfect square: 15 × 15 = 225, so √225 is exactly 15. No estimating needed.
| k | k² | Compared to 225 |
|---|---|---|
| 13 | 169 | 56 below |
| 14 | 196 | 29 below |
| 15 | 225 | equal |
| 16 | 256 | 31 above |
| 17 | 289 | 64 above |
| 18 | 324 | 99 above |
Exact form from the prime factors
225 = 3^2 × 5^2. Every prime appears an even number of times, so the whole thing comes out of the square root: √225 = 15.
Frequently Asked Questions
What is the square root of 225?
The square root of 225 is exactly 15.
Is 225 a perfect square?
Yes, 225 is a perfect square. Its square root, 15, is a whole number.
What two whole numbers is √225 between?
None needed -- √225 is exactly 15, a whole number. For context, the perfect squares just before and after 225 are 196 (14²) and 256 (16²).
What are the square roots of the numbers right next to 225?
√224 is about 14.9666, and √226 is about 15.0333. 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 √225 squared?
Exactly 225 -- squaring undoes the square root. Squaring the rounded decimal 15 gives 225, which is why the radical form 15 is the exact answer and the decimal is an approximation.
What is the negative square root of 225?
−15. Every positive number has two square roots, one positive and one negative, because (−15)² is also 225. The radical sign √ by convention means the positive one.
More Number Theory
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