Square Root of 49
The square root of 49 is exactly 7. Yes, 49 is a perfect square. Its square root, 7, is a whole number.
Where √49 sits
49 is a perfect square: 7 × 7 = 49, so √49 is exactly 7. No estimating needed.
| k | k² | Compared to 49 |
|---|---|---|
| 5 | 25 | 24 below |
| 6 | 36 | 13 below |
| 7 | 49 | equal |
| 8 | 64 | 15 above |
| 9 | 81 | 32 above |
| 10 | 100 | 51 above |
Exact form from the prime factors
49 = 7^2. Every prime appears an even number of times, so the whole thing comes out of the square root: √49 = 7.
Frequently Asked Questions
What is the square root of 49?
The square root of 49 is exactly 7.
Is 49 a perfect square?
Yes, 49 is a perfect square. Its square root, 7, is a whole number.
What two whole numbers is √49 between?
None needed -- √49 is exactly 7, a whole number. For context, the perfect squares just before and after 49 are 36 (6²) and 64 (8²).
What are the square roots of the numbers right next to 49?
√48 is about 6.9282, and √50 is about 7.0711. 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 √49 squared?
Exactly 49 -- squaring undoes the square root. Squaring the rounded decimal 7 gives 49, which is why the radical form 7 is the exact answer and the decimal is an approximation.
What is the negative square root of 49?
−7. Every positive number has two square roots, one positive and one negative, because (−7)² is also 49. The radical sign √ by convention means the positive one.
More Number Theory
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