Square Root of 400
The square root of 400 is exactly 20. Yes, 400 is a perfect square. Its square root, 20, is a whole number.
Where √400 sits
400 is a perfect square: 20 × 20 = 400, so √400 is exactly 20. No estimating needed.
| k | k² | Compared to 400 |
|---|---|---|
| 18 | 324 | 76 below |
| 19 | 361 | 39 below |
| 20 | 400 | equal |
| 21 | 441 | 41 above |
| 22 | 484 | 84 above |
| 23 | 529 | 129 above |
Exact form from the prime factors
400 = 2^4 × 5^2. Every prime appears an even number of times, so the whole thing comes out of the square root: √400 = 20.
Frequently Asked Questions
What is the square root of 400?
The square root of 400 is exactly 20.
Is 400 a perfect square?
Yes, 400 is a perfect square. Its square root, 20, is a whole number.
What two whole numbers is √400 between?
None needed -- √400 is exactly 20, a whole number. For context, the perfect squares just before and after 400 are 361 (19²) and 441 (21²).
What are the square roots of the numbers right next to 400?
√399 is about 19.975, and √401 is about 20.025. 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 √400 squared?
Exactly 400 -- squaring undoes the square root. Squaring the rounded decimal 20 gives 400, which is why the radical form 20 is the exact answer and the decimal is an approximation.
What is the negative square root of 400?
−20. Every positive number has two square roots, one positive and one negative, because (−20)² is also 400. The radical sign √ by convention means the positive one.
More Number Theory
- Square Root Calculator (look up any number)
- GCF Calculator
- LCM Calculator