Square Root Calculator › Square root of 33
Square Root of 33
√33 ≈ 5.744563
33 is not a perfect square, so √33 is an irrational number that is approximately 5.744563. In simplified radical form, √33 = √33.
√33 lies between √25 = 5 and √36 = 6.
| Number | 33 |
| Square root (decimal) | 5.744563 |
| Simplified radical | √33 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 33
33 = 3 × 11. This is what determines the simplified radical: for √33 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √33 is already in simplest radical form as √33.
Estimating √33 by hand
√33 falls between √25 = 5 and √36 = 6, so it starts at 5.something. The Babylonian method refines that guess by averaging it with 33 ÷ the guess:
| Step | Estimate |
| Start | 5 |
| Step 1 | 5.8 |
| Step 2 | 5.744828 |
| Step 3 | 5.744563 |
After 3 steps the estimate is 5.744563, matching √33 ≈ 5.744563.
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Frequently asked questions
Is 33 a perfect square?
No, 33 is not a perfect square, so its square root is irrational and approximately 5.744563.
What is the square root of 33 in simplest radical form?
√33 = √33 in simplest radical form.