Square Root Calculator › Square root of 426
Square Root of 426
√426 ≈ 20.639767
426 is not a perfect square, so √426 is an irrational number that is approximately 20.639767. In simplified radical form, √426 = √426.
√426 lies between √400 = 20 and √441 = 21.
| Number | 426 |
| Square root (decimal) | 20.639767 |
| Simplified radical | √426 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 426
426 = 2 × 3 × 71. This is what determines the simplified radical: for √426 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √426 is already in simplest radical form as √426.
Estimating √426 by hand
√426 falls between √400 = 20 and √441 = 21, so it starts at 20.something. The Babylonian method refines that guess by averaging it with 426 ÷ the guess:
| Step | Estimate |
| Start | 20 |
| Step 1 | 20.65 |
| Step 2 | 20.63977 |
| Step 3 | 20.639767 |
After 3 steps the estimate is 20.639767, matching √426 ≈ 20.639767.
Nearby square roots
Frequently asked questions
Is 426 a perfect square?
No, 426 is not a perfect square, so its square root is irrational and approximately 20.639767.
What is the square root of 426 in simplest radical form?
√426 = √426 in simplest radical form.