Square Root Calculator › Square root of 101
Square Root of 101
√101 ≈ 10.049876
101 is not a perfect square, so √101 is an irrational number that is approximately 10.049876. In simplified radical form, √101 = √101.
√101 lies between √100 = 10 and √121 = 11.
| Number | 101 |
| Square root (decimal) | 10.049876 |
| Simplified radical | √101 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 101
101 = 101. This is what determines the simplified radical: for √101 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √101 is already in simplest radical form as √101.
Estimating √101 by hand
√101 falls between √100 = 10 and √121 = 11, so it starts at 10.something. The Babylonian method refines that guess by averaging it with 101 ÷ the guess:
| Step | Estimate |
| Start | 10 |
| Step 1 | 10.05 |
| Step 2 | 10.049876 |
| Step 3 | 10.049876 |
After 3 steps the estimate is 10.049876, matching √101 ≈ 10.049876.
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Frequently asked questions
Is 101 a perfect square?
No, 101 is not a perfect square, so its square root is irrational and approximately 10.049876.
What is the square root of 101 in simplest radical form?
√101 = √101 in simplest radical form.