Square Root Calculator › Square root of 17
Square Root of 17
√17 ≈ 4.123106
17 is not a perfect square, so √17 is an irrational number that is approximately 4.123106. In simplified radical form, √17 = √17.
√17 lies between √16 = 4 and √25 = 5.
| Number | 17 |
| Square root (decimal) | 4.123106 |
| Simplified radical | √17 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 17
17 = 17. This is what determines the simplified radical: for √17 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √17 is already in simplest radical form as √17.
Estimating √17 by hand
√17 falls between √16 = 4 and √25 = 5, so it starts at 4.something. The Babylonian method refines that guess by averaging it with 17 ÷ the guess:
| Step | Estimate |
| Start | 4 |
| Step 1 | 4.125 |
| Step 2 | 4.123106 |
| Step 3 | 4.123106 |
After 3 steps the estimate is 4.123106, matching √17 ≈ 4.123106.
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Frequently asked questions
Is 17 a perfect square?
No, 17 is not a perfect square, so its square root is irrational and approximately 4.123106.
What is the square root of 17 in simplest radical form?
√17 = √17 in simplest radical form.