Square Root Calculator › Square root of 302
Square Root of 302
√302 ≈ 17.378147
302 is not a perfect square, so √302 is an irrational number that is approximately 17.378147. In simplified radical form, √302 = √302.
√302 lies between √289 = 17 and √324 = 18.
| Number | 302 |
| Square root (decimal) | 17.378147 |
| Simplified radical | √302 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 302
302 = 2 × 151. This is what determines the simplified radical: for √302 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √302 is already in simplest radical form as √302.
Estimating √302 by hand
√302 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 302 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.382353 |
| Step 2 | 17.378148 |
| Step 3 | 17.378147 |
After 3 steps the estimate is 17.378147, matching √302 ≈ 17.378147.
Nearby square roots
Frequently asked questions
Is 302 a perfect square?
No, 302 is not a perfect square, so its square root is irrational and approximately 17.378147.
What is the square root of 302 in simplest radical form?
√302 = √302 in simplest radical form.