Square Root Calculator › Square root of 305
Square Root of 305
√305 ≈ 17.464249
305 is not a perfect square, so √305 is an irrational number that is approximately 17.464249. In simplified radical form, √305 = √305.
√305 lies between √289 = 17 and √324 = 18.
| Number | 305 |
| Square root (decimal) | 17.464249 |
| Simplified radical | √305 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 305
305 = 5 × 61. This is what determines the simplified radical: for √305 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √305 is already in simplest radical form as √305.
Estimating √305 by hand
√305 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 305 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.470588 |
| Step 2 | 17.46425 |
| Step 3 | 17.464249 |
After 3 steps the estimate is 17.464249, matching √305 ≈ 17.464249.
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Frequently asked questions
Is 305 a perfect square?
No, 305 is not a perfect square, so its square root is irrational and approximately 17.464249.
What is the square root of 305 in simplest radical form?
√305 = √305 in simplest radical form.