Square Root Calculator › Square root of 59
Square Root of 59
√59 ≈ 7.681146
59 is not a perfect square, so √59 is an irrational number that is approximately 7.681146. In simplified radical form, √59 = √59.
√59 lies between √49 = 7 and √64 = 8.
| Number | 59 |
| Square root (decimal) | 7.681146 |
| Simplified radical | √59 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 59
59 = 59. This is what determines the simplified radical: for √59 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √59 is already in simplest radical form as √59.
Estimating √59 by hand
√59 falls between √49 = 7 and √64 = 8, so it starts at 7.something. The Babylonian method refines that guess by averaging it with 59 ÷ the guess:
| Step | Estimate |
| Start | 7 |
| Step 1 | 7.714286 |
| Step 2 | 7.681217 |
| Step 3 | 7.681146 |
After 3 steps the estimate is 7.681146, matching √59 ≈ 7.681146.
Nearby square roots
Frequently asked questions
Is 59 a perfect square?
No, 59 is not a perfect square, so its square root is irrational and approximately 7.681146.
What is the square root of 59 in simplest radical form?
√59 = √59 in simplest radical form.