Square Root Calculator › Square root of 34
Square Root of 34
√34 ≈ 5.830952
34 is not a perfect square, so √34 is an irrational number that is approximately 5.830952. In simplified radical form, √34 = √34.
√34 lies between √25 = 5 and √36 = 6.
| Number | 34 |
| Square root (decimal) | 5.830952 |
| Simplified radical | √34 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 34
34 = 2 × 17. This is what determines the simplified radical: for √34 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √34 is already in simplest radical form as √34.
Estimating √34 by hand
√34 falls between √25 = 5 and √36 = 6, so it starts at 5.something. The Babylonian method refines that guess by averaging it with 34 ÷ the guess:
| Step | Estimate |
| Start | 5 |
| Step 1 | 5.9 |
| Step 2 | 5.831356 |
| Step 3 | 5.830952 |
After 3 steps the estimate is 5.830952, matching √34 ≈ 5.830952.
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Frequently asked questions
Is 34 a perfect square?
No, 34 is not a perfect square, so its square root is irrational and approximately 5.830952.
What is the square root of 34 in simplest radical form?
√34 = √34 in simplest radical form.