Square Root Calculator › Square root of 27
Square Root of 27
√27 ≈ 5.196152
27 is not a perfect square, so √27 is an irrational number that is approximately 5.196152. In simplified radical form, √27 = 3√3.
√27 lies between √25 = 5 and √36 = 6.
| Number | 27 |
| Square root (decimal) | 5.196152 |
| Simplified radical | 3√3 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 27
27 = 3^3. This is what determines the simplified radical: for √27 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √27 = 3√3.
Estimating √27 by hand
√27 falls between √25 = 5 and √36 = 6, so it starts at 5.something. The Babylonian method refines that guess by averaging it with 27 ÷ the guess:
| Step | Estimate |
| Start | 5 |
| Step 1 | 5.2 |
| Step 2 | 5.196154 |
| Step 3 | 5.196152 |
After 3 steps the estimate is 5.196152, matching √27 ≈ 5.196152.
Nearby square roots
Frequently asked questions
Is 27 a perfect square?
No, 27 is not a perfect square, so its square root is irrational and approximately 5.196152.
What is the square root of 27 in simplest radical form?
√27 = 3√3 in simplest radical form.