Square Root Calculator › Square root of 258
Square Root of 258
√258 ≈ 16.062378
258 is not a perfect square, so √258 is an irrational number that is approximately 16.062378. In simplified radical form, √258 = √258.
√258 lies between √256 = 16 and √289 = 17.
| Number | 258 |
| Square root (decimal) | 16.062378 |
| Simplified radical | √258 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 258
258 = 2 × 3 × 43. This is what determines the simplified radical: for √258 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √258 is already in simplest radical form as √258.
Estimating √258 by hand
√258 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 258 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.0625 |
| Step 2 | 16.062378 |
| Step 3 | 16.062378 |
After 3 steps the estimate is 16.062378, matching √258 ≈ 16.062378.
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Frequently asked questions
Is 258 a perfect square?
No, 258 is not a perfect square, so its square root is irrational and approximately 16.062378.
What is the square root of 258 in simplest radical form?
√258 = √258 in simplest radical form.