Square Root Calculator › Square root of 35
Square Root of 35
√35 ≈ 5.91608
35 is not a perfect square, so √35 is an irrational number that is approximately 5.91608. In simplified radical form, √35 = √35.
√35 lies between √25 = 5 and √36 = 6.
| Number | 35 |
| Square root (decimal) | 5.91608 |
| Simplified radical | √35 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 35
35 = 5 × 7. This is what determines the simplified radical: for √35 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √35 is already in simplest radical form as √35.
Estimating √35 by hand
√35 falls between √25 = 5 and √36 = 6, so it starts at 5.something. The Babylonian method refines that guess by averaging it with 35 ÷ the guess:
| Step | Estimate |
| Start | 5 |
| Step 1 | 6 |
| Step 2 | 5.916667 |
| Step 3 | 5.91608 |
After 3 steps the estimate is 5.91608, matching √35 ≈ 5.91608.
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Frequently asked questions
Is 35 a perfect square?
No, 35 is not a perfect square, so its square root is irrational and approximately 5.91608.
What is the square root of 35 in simplest radical form?
√35 = √35 in simplest radical form.