Square Root of 64
The square root of 64 is exactly 8. Yes, 64 is a perfect square. Its square root, 8, is a whole number.
Where √64 sits
64 is a perfect square: 8 × 8 = 64, so √64 is exactly 8. No estimating needed.
| k | k² | Compared to 64 |
|---|---|---|
| 6 | 36 | 28 below |
| 7 | 49 | 15 below |
| 8 | 64 | equal |
| 9 | 81 | 17 above |
| 10 | 100 | 36 above |
| 11 | 121 | 57 above |
Exact form from the prime factors
64 = 2^6. Every prime appears an even number of times, so the whole thing comes out of the square root: √64 = 8.
Frequently Asked Questions
What is the square root of 64?
The square root of 64 is exactly 8.
Is 64 a perfect square?
Yes, 64 is a perfect square. Its square root, 8, is a whole number.
What two whole numbers is √64 between?
None needed -- √64 is exactly 8, a whole number. For context, the perfect squares just before and after 64 are 49 (7²) and 81 (9²).
What are the square roots of the numbers right next to 64?
√63 is about 7.9373, and √65 is about 8.0623. 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 √64 squared?
Exactly 64 -- squaring undoes the square root. Squaring the rounded decimal 8 gives 64, which is why the radical form 8 is the exact answer and the decimal is an approximation.
What is the negative square root of 64?
−8. Every positive number has two square roots, one positive and one negative, because (−8)² is also 64. The radical sign √ by convention means the positive one.
More Number Theory
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