Square Root Calculator › Square root of 99
Square Root of 99
√99 ≈ 9.949874
99 is not a perfect square, so √99 is an irrational number that is approximately 9.949874. In simplified radical form, √99 = 3√11.
√99 lies between √81 = 9 and √100 = 10.
| Number | 99 |
| Square root (decimal) | 9.949874 |
| Simplified radical | 3√11 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 99
99 = 3^2 × 11. This is what determines the simplified radical: for √99 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √99 = 3√11.
Estimating √99 by hand
√99 falls between √81 = 9 and √100 = 10, so it starts at 9.something. The Babylonian method refines that guess by averaging it with 99 ÷ the guess:
| Step | Estimate |
| Start | 9 |
| Step 1 | 10 |
| Step 2 | 9.95 |
| Step 3 | 9.949874 |
After 3 steps the estimate is 9.949874, matching √99 ≈ 9.949874.
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Frequently asked questions
Is 99 a perfect square?
No, 99 is not a perfect square, so its square root is irrational and approximately 9.949874.
What is the square root of 99 in simplest radical form?
√99 = 3√11 in simplest radical form.