Square Root of 196
The square root of 196 is exactly 14. Yes, 196 is a perfect square. Its square root, 14, is a whole number.
Where √196 sits
196 is a perfect square: 14 × 14 = 196, so √196 is exactly 14. No estimating needed.
| k | k² | Compared to 196 |
|---|---|---|
| 12 | 144 | 52 below |
| 13 | 169 | 27 below |
| 14 | 196 | equal |
| 15 | 225 | 29 above |
| 16 | 256 | 60 above |
| 17 | 289 | 93 above |
Exact form from the prime factors
196 = 2^2 × 7^2. Every prime appears an even number of times, so the whole thing comes out of the square root: √196 = 14.
Frequently Asked Questions
What is the square root of 196?
The square root of 196 is exactly 14.
Is 196 a perfect square?
Yes, 196 is a perfect square. Its square root, 14, is a whole number.
What two whole numbers is √196 between?
None needed -- √196 is exactly 14, a whole number. For context, the perfect squares just before and after 196 are 169 (13²) and 225 (15²).
What are the square roots of the numbers right next to 196?
√195 is about 13.9642, and √197 is about 14.0357. 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 √196 squared?
Exactly 196 -- squaring undoes the square root. Squaring the rounded decimal 14 gives 196, which is why the radical form 14 is the exact answer and the decimal is an approximation.
What is the negative square root of 196?
−14. Every positive number has two square roots, one positive and one negative, because (−14)² is also 196. The radical sign √ by convention means the positive one.
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