Square Root Calculator › Square root of 487
Square Root of 487
√487 ≈ 22.068076
487 is not a perfect square, so √487 is an irrational number that is approximately 22.068076. In simplified radical form, √487 = √487.
√487 lies between √484 = 22 and √529 = 23.
| Number | 487 |
| Square root (decimal) | 22.068076 |
| Simplified radical | √487 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 487
487 = 487. This is what determines the simplified radical: for √487 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √487 is already in simplest radical form as √487.
Estimating √487 by hand
√487 falls between √484 = 22 and √529 = 23, so it starts at 22.something. The Babylonian method refines that guess by averaging it with 487 ÷ the guess:
| Step | Estimate |
| Start | 22 |
| Step 1 | 22.068182 |
| Step 2 | 22.068076 |
| Step 3 | 22.068076 |
After 3 steps the estimate is 22.068076, matching √487 ≈ 22.068076.
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Frequently asked questions
Is 487 a perfect square?
No, 487 is not a perfect square, so its square root is irrational and approximately 22.068076.
What is the square root of 487 in simplest radical form?
√487 = √487 in simplest radical form.