Square Root Calculator › Square root of 58
Square Root of 58
√58 ≈ 7.615773
58 is not a perfect square, so √58 is an irrational number that is approximately 7.615773. In simplified radical form, √58 = √58.
√58 lies between √49 = 7 and √64 = 8.
| Number | 58 |
| Square root (decimal) | 7.615773 |
| Simplified radical | √58 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 58
58 = 2 × 29. This is what determines the simplified radical: for √58 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √58 is already in simplest radical form as √58.
Estimating √58 by hand
√58 falls between √49 = 7 and √64 = 8, so it starts at 7.something. The Babylonian method refines that guess by averaging it with 58 ÷ the guess:
| Step | Estimate |
| Start | 7 |
| Step 1 | 7.642857 |
| Step 2 | 7.615821 |
| Step 3 | 7.615773 |
After 3 steps the estimate is 7.615773, matching √58 ≈ 7.615773.
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Frequently asked questions
Is 58 a perfect square?
No, 58 is not a perfect square, so its square root is irrational and approximately 7.615773.
What is the square root of 58 in simplest radical form?
√58 = √58 in simplest radical form.