Square Root Calculator › Square root of 29
Square Root of 29
√29 ≈ 5.385165
29 is not a perfect square, so √29 is an irrational number that is approximately 5.385165. In simplified radical form, √29 = √29.
√29 lies between √25 = 5 and √36 = 6.
| Number | 29 |
| Square root (decimal) | 5.385165 |
| Simplified radical | √29 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 29
29 = 29. This is what determines the simplified radical: for √29 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √29 is already in simplest radical form as √29.
Estimating √29 by hand
√29 falls between √25 = 5 and √36 = 6, so it starts at 5.something. The Babylonian method refines that guess by averaging it with 29 ÷ the guess:
| Step | Estimate |
| Start | 5 |
| Step 1 | 5.4 |
| Step 2 | 5.385185 |
| Step 3 | 5.385165 |
After 3 steps the estimate is 5.385165, matching √29 ≈ 5.385165.
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Frequently asked questions
Is 29 a perfect square?
No, 29 is not a perfect square, so its square root is irrational and approximately 5.385165.
What is the square root of 29 in simplest radical form?
√29 = √29 in simplest radical form.