Square Root Calculator › Square root of 14
Square Root of 14
√14 ≈ 3.741657
14 is not a perfect square, so √14 is an irrational number that is approximately 3.741657. In simplified radical form, √14 = √14.
√14 lies between √9 = 3 and √16 = 4.
| Number | 14 |
| Square root (decimal) | 3.741657 |
| Simplified radical | √14 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 14
14 = 2 × 7. This is what determines the simplified radical: for √14 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √14 is already in simplest radical form as √14.
Estimating √14 by hand
√14 falls between √9 = 3 and √16 = 4, so it starts at 3.something. The Babylonian method refines that guess by averaging it with 14 ÷ the guess:
| Step | Estimate |
| Start | 3 |
| Step 1 | 3.833333 |
| Step 2 | 3.742754 |
| Step 3 | 3.741658 |
After 3 steps the estimate is 3.741658, matching √14 ≈ 3.741657.
Nearby square roots
Frequently asked questions
Is 14 a perfect square?
No, 14 is not a perfect square, so its square root is irrational and approximately 3.741657.
What is the square root of 14 in simplest radical form?
√14 = √14 in simplest radical form.