Square Root Calculator › Square root of 87
Square Root of 87
√87 ≈ 9.327379
87 is not a perfect square, so √87 is an irrational number that is approximately 9.327379. In simplified radical form, √87 = √87.
√87 lies between √81 = 9 and √100 = 10.
| Number | 87 |
| Square root (decimal) | 9.327379 |
| Simplified radical | √87 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 87
87 = 3 × 29. This is what determines the simplified radical: for √87 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √87 is already in simplest radical form as √87.
Estimating √87 by hand
√87 falls between √81 = 9 and √100 = 10, so it starts at 9.something. The Babylonian method refines that guess by averaging it with 87 ÷ the guess:
| Step | Estimate |
| Start | 9 |
| Step 1 | 9.333333 |
| Step 2 | 9.327381 |
| Step 3 | 9.327379 |
After 3 steps the estimate is 9.327379, matching √87 ≈ 9.327379.
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Frequently asked questions
Is 87 a perfect square?
No, 87 is not a perfect square, so its square root is irrational and approximately 9.327379.
What is the square root of 87 in simplest radical form?
√87 = √87 in simplest radical form.