Square Root Calculator › Square root of 428
Square Root of 428
√428 ≈ 20.688161
428 is not a perfect square, so √428 is an irrational number that is approximately 20.688161. In simplified radical form, √428 = 2√107.
√428 lies between √400 = 20 and √441 = 21.
| Number | 428 |
| Square root (decimal) | 20.688161 |
| Simplified radical | 2√107 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 428
428 = 2^2 × 107. This is what determines the simplified radical: for √428 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √428 = 2√107.
Estimating √428 by hand
√428 falls between √400 = 20 and √441 = 21, so it starts at 20.something. The Babylonian method refines that guess by averaging it with 428 ÷ the guess:
| Step | Estimate |
| Start | 20 |
| Step 1 | 20.7 |
| Step 2 | 20.688164 |
| Step 3 | 20.688161 |
After 3 steps the estimate is 20.688161, matching √428 ≈ 20.688161.
Nearby square roots
Frequently asked questions
Is 428 a perfect square?
No, 428 is not a perfect square, so its square root is irrational and approximately 20.688161.
What is the square root of 428 in simplest radical form?
√428 = 2√107 in simplest radical form.