Square Root Calculator › Square root of 475
Square Root of 475
√475 ≈ 21.794495
475 is not a perfect square, so √475 is an irrational number that is approximately 21.794495. In simplified radical form, √475 = 5√19.
√475 lies between √441 = 21 and √484 = 22.
| Number | 475 |
| Square root (decimal) | 21.794495 |
| Simplified radical | 5√19 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 475
475 = 5^2 × 19. This is what determines the simplified radical: for √475 you pull out one copy of any prime that appears twice.
Here the paired factor 5 comes out from under the root, leaving √475 = 5√19.
Estimating √475 by hand
√475 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 475 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.809524 |
| Step 2 | 21.7945 |
| Step 3 | 21.794495 |
After 3 steps the estimate is 21.794495, matching √475 ≈ 21.794495.
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Frequently asked questions
Is 475 a perfect square?
No, 475 is not a perfect square, so its square root is irrational and approximately 21.794495.
What is the square root of 475 in simplest radical form?
√475 = 5√19 in simplest radical form.