Square Root Calculator › Square root of 472
Square Root of 472
√472 ≈ 21.725561
472 is not a perfect square, so √472 is an irrational number that is approximately 21.725561. In simplified radical form, √472 = 2√118.
√472 lies between √441 = 21 and √484 = 22.
| Number | 472 |
| Square root (decimal) | 21.725561 |
| Simplified radical | 2√118 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 472
472 = 2^3 × 59. This is what determines the simplified radical: for √472 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √472 = 2√118.
Estimating √472 by hand
√472 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 472 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.738095 |
| Step 2 | 21.725565 |
| Step 3 | 21.725561 |
After 3 steps the estimate is 21.725561, matching √472 ≈ 21.725561.
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Frequently asked questions
Is 472 a perfect square?
No, 472 is not a perfect square, so its square root is irrational and approximately 21.725561.
What is the square root of 472 in simplest radical form?
√472 = 2√118 in simplest radical form.