Square Root Calculator › Square root of 303
Square Root of 303
√303 ≈ 17.406895
303 is not a perfect square, so √303 is an irrational number that is approximately 17.406895. In simplified radical form, √303 = √303.
√303 lies between √289 = 17 and √324 = 18.
| Number | 303 |
| Square root (decimal) | 17.406895 |
| Simplified radical | √303 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 303
303 = 3 × 101. This is what determines the simplified radical: for √303 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √303 is already in simplest radical form as √303.
Estimating √303 by hand
√303 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 303 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.411765 |
| Step 2 | 17.406896 |
| Step 3 | 17.406895 |
After 3 steps the estimate is 17.406895, matching √303 ≈ 17.406895.
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Frequently asked questions
Is 303 a perfect square?
No, 303 is not a perfect square, so its square root is irrational and approximately 17.406895.
What is the square root of 303 in simplest radical form?
√303 = √303 in simplest radical form.