Square Root Calculator › Square root of 424
Square Root of 424
√424 ≈ 20.59126
424 is not a perfect square, so √424 is an irrational number that is approximately 20.59126. In simplified radical form, √424 = 2√106.
√424 lies between √400 = 20 and √441 = 21.
| Number | 424 |
| Square root (decimal) | 20.59126 |
| Simplified radical | 2√106 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 424
424 = 2^3 × 53. This is what determines the simplified radical: for √424 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √424 = 2√106.
Estimating √424 by hand
√424 falls between √400 = 20 and √441 = 21, so it starts at 20.something. The Babylonian method refines that guess by averaging it with 424 ÷ the guess:
| Step | Estimate |
| Start | 20 |
| Step 1 | 20.6 |
| Step 2 | 20.591262 |
| Step 3 | 20.59126 |
After 3 steps the estimate is 20.59126, matching √424 ≈ 20.59126.
Nearby square roots
Frequently asked questions
Is 424 a perfect square?
No, 424 is not a perfect square, so its square root is irrational and approximately 20.59126.
What is the square root of 424 in simplest radical form?
√424 = 2√106 in simplest radical form.