Square Root Calculator › Square root of 30
Square Root of 30
√30 ≈ 5.477226
30 is not a perfect square, so √30 is an irrational number that is approximately 5.477226. In simplified radical form, √30 = √30.
√30 lies between √25 = 5 and √36 = 6.
| Number | 30 |
| Square root (decimal) | 5.477226 |
| Simplified radical | √30 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 30
30 = 2 × 3 × 5. This is what determines the simplified radical: for √30 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √30 is already in simplest radical form as √30.
Estimating √30 by hand
√30 falls between √25 = 5 and √36 = 6, so it starts at 5.something. The Babylonian method refines that guess by averaging it with 30 ÷ the guess:
| Step | Estimate |
| Start | 5 |
| Step 1 | 5.5 |
| Step 2 | 5.477273 |
| Step 3 | 5.477226 |
After 3 steps the estimate is 5.477226, matching √30 ≈ 5.477226.
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Frequently asked questions
Is 30 a perfect square?
No, 30 is not a perfect square, so its square root is irrational and approximately 5.477226.
What is the square root of 30 in simplest radical form?
√30 = √30 in simplest radical form.