Square Root Calculator › Square root of 470
Square Root of 470
√470 ≈ 21.679483
470 is not a perfect square, so √470 is an irrational number that is approximately 21.679483. In simplified radical form, √470 = √470.
√470 lies between √441 = 21 and √484 = 22.
| Number | 470 |
| Square root (decimal) | 21.679483 |
| Simplified radical | √470 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 470
470 = 2 × 5 × 47. This is what determines the simplified radical: for √470 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √470 is already in simplest radical form as √470.
Estimating √470 by hand
√470 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 470 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.690476 |
| Step 2 | 21.679486 |
| Step 3 | 21.679483 |
After 3 steps the estimate is 21.679483, matching √470 ≈ 21.679483.
Nearby square roots
Frequently asked questions
Is 470 a perfect square?
No, 470 is not a perfect square, so its square root is irrational and approximately 21.679483.
What is the square root of 470 in simplest radical form?
√470 = √470 in simplest radical form.