Square Root Calculator › Square root of 300
Square Root of 300
√300 ≈ 17.320508
300 is not a perfect square, so √300 is an irrational number that is approximately 17.320508. In simplified radical form, √300 = 10√3.
√300 lies between √289 = 17 and √324 = 18.
| Number | 300 |
| Square root (decimal) | 17.320508 |
| Simplified radical | 10√3 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 300
300 = 2^2 × 3 × 5^2. This is what determines the simplified radical: for √300 you pull out one copy of any prime that appears twice.
Here the paired factors 2 and 5 come out from under the root, leaving √300 = 10√3.
Estimating √300 by hand
√300 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 300 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.323529 |
| Step 2 | 17.320508 |
| Step 3 | 17.320508 |
After 3 steps the estimate is 17.320508, matching √300 ≈ 17.320508.
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Frequently asked questions
Is 300 a perfect square?
No, 300 is not a perfect square, so its square root is irrational and approximately 17.320508.
What is the square root of 300 in simplest radical form?
√300 = 10√3 in simplest radical form.