Square Root of 100
The square root of 100 is exactly 10. Yes, 100 is a perfect square. Its square root, 10, is a whole number.
Where √100 sits
100 is a perfect square: 10 × 10 = 100, so √100 is exactly 10. No estimating needed.
| k | k² | Compared to 100 |
|---|---|---|
| 8 | 64 | 36 below |
| 9 | 81 | 19 below |
| 10 | 100 | equal |
| 11 | 121 | 21 above |
| 12 | 144 | 44 above |
| 13 | 169 | 69 above |
Exact form from the prime factors
100 = 2^2 × 5^2. Every prime appears an even number of times, so the whole thing comes out of the square root: √100 = 10.
Frequently Asked Questions
What is the square root of 100?
The square root of 100 is exactly 10.
Is 100 a perfect square?
Yes, 100 is a perfect square. Its square root, 10, is a whole number.
What two whole numbers is √100 between?
None needed -- √100 is exactly 10, a whole number. For context, the perfect squares just before and after 100 are 81 (9²) and 121 (11²).
What are the square roots of the numbers right next to 100?
√99 is about 9.9499, and √101 is about 10.0499. 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 √100 squared?
Exactly 100 -- squaring undoes the square root. Squaring the rounded decimal 10 gives 100, which is why the radical form 10 is the exact answer and the decimal is an approximation.
What is the negative square root of 100?
−10. Every positive number has two square roots, one positive and one negative, because (−10)² is also 100. The radical sign √ by convention means the positive one.
More Number Theory
- Square Root Calculator (look up any number)
- Factors of 100
- GCF Calculator
- LCM Calculator