Square Root Calculator › Square root of 476
Square Root of 476
√476 ≈ 21.817424
476 is not a perfect square, so √476 is an irrational number that is approximately 21.817424. In simplified radical form, √476 = 2√119.
√476 lies between √441 = 21 and √484 = 22.
| Number | 476 |
| Square root (decimal) | 21.817424 |
| Simplified radical | 2√119 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 476
476 = 2^2 × 7 × 17. This is what determines the simplified radical: for √476 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √476 = 2√119.
Estimating √476 by hand
√476 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 476 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.833333 |
| Step 2 | 21.81743 |
| Step 3 | 21.817424 |
After 3 steps the estimate is 21.817424, matching √476 ≈ 21.817424.
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Frequently asked questions
Is 476 a perfect square?
No, 476 is not a perfect square, so its square root is irrational and approximately 21.817424.
What is the square root of 476 in simplest radical form?
√476 = 2√119 in simplest radical form.