Square Root of 169
The square root of 169 is exactly 13. Yes, 169 is a perfect square. Its square root, 13, is a whole number.
Where √169 sits
169 is a perfect square: 13 × 13 = 169, so √169 is exactly 13. No estimating needed.
| k | k² | Compared to 169 |
|---|---|---|
| 11 | 121 | 48 below |
| 12 | 144 | 25 below |
| 13 | 169 | equal |
| 14 | 196 | 27 above |
| 15 | 225 | 56 above |
| 16 | 256 | 87 above |
Exact form from the prime factors
169 = 13^2. Every prime appears an even number of times, so the whole thing comes out of the square root: √169 = 13.
Frequently Asked Questions
What is the square root of 169?
The square root of 169 is exactly 13.
Is 169 a perfect square?
Yes, 169 is a perfect square. Its square root, 13, is a whole number.
What two whole numbers is √169 between?
None needed -- √169 is exactly 13, a whole number. For context, the perfect squares just before and after 169 are 144 (12²) and 196 (14²).
What are the square roots of the numbers right next to 169?
√168 is about 12.9615, and √170 is about 13.0384. 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 √169 squared?
Exactly 169 -- squaring undoes the square root. Squaring the rounded decimal 13 gives 169, which is why the radical form 13 is the exact answer and the decimal is an approximation.
What is the negative square root of 169?
−13. Every positive number has two square roots, one positive and one negative, because (−13)² is also 169. The radical sign √ by convention means the positive one.
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