Square Root of 4
The square root of 4 is exactly 2. Yes, 4 is a perfect square. Its square root, 2, is a whole number.
Where √4 sits
4 is a perfect square: 2 × 2 = 4, so √4 is exactly 2. No estimating needed.
| k | k² | Compared to 4 |
|---|---|---|
| 1 | 1 | 3 below |
| 2 | 4 | equal |
| 3 | 9 | 5 above |
| 4 | 16 | 12 above |
| 5 | 25 | 21 above |
| 6 | 36 | 32 above |
Exact form from the prime factors
4 = 2^2. Every prime appears an even number of times, so the whole thing comes out of the square root: √4 = 2.
Frequently Asked Questions
What is the square root of 4?
The square root of 4 is exactly 2.
Is 4 a perfect square?
Yes, 4 is a perfect square. Its square root, 2, is a whole number.
What two whole numbers is √4 between?
None needed -- √4 is exactly 2, a whole number. For context, the perfect squares just before and after 4 are 1 (1²) and 9 (3²).
What are the square roots of the numbers right next to 4?
√3 is about 1.7321, and √5 is about 2.2361. 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 √4 squared?
Exactly 4 -- squaring undoes the square root. Squaring the rounded decimal 2 gives 4, which is why the radical form 2 is the exact answer and the decimal is an approximation.
What is the negative square root of 4?
−2. Every positive number has two square roots, one positive and one negative, because (−2)² is also 4. The radical sign √ by convention means the positive one.
More Number Theory
- Square Root Calculator (look up any number)
- Factors of 4
- GCF Calculator
- LCM Calculator