Square Root Calculator › Square root of 102
Square Root of 102
√102 ≈ 10.099505
102 is not a perfect square, so √102 is an irrational number that is approximately 10.099505. In simplified radical form, √102 = √102.
√102 lies between √100 = 10 and √121 = 11.
| Number | 102 |
| Square root (decimal) | 10.099505 |
| Simplified radical | √102 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 102
102 = 2 × 3 × 17. This is what determines the simplified radical: for √102 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √102 is already in simplest radical form as √102.
Estimating √102 by hand
√102 falls between √100 = 10 and √121 = 11, so it starts at 10.something. The Babylonian method refines that guess by averaging it with 102 ÷ the guess:
| Step | Estimate |
| Start | 10 |
| Step 1 | 10.1 |
| Step 2 | 10.099505 |
| Step 3 | 10.099505 |
After 3 steps the estimate is 10.099505, matching √102 ≈ 10.099505.
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Frequently asked questions
Is 102 a perfect square?
No, 102 is not a perfect square, so its square root is irrational and approximately 10.099505.
What is the square root of 102 in simplest radical form?
√102 = √102 in simplest radical form.