Square Root Calculator › Square root of 398
Square Root of 398
√398 ≈ 19.949937
398 is not a perfect square, so √398 is an irrational number that is approximately 19.949937. In simplified radical form, √398 = √398.
√398 lies between √361 = 19 and √400 = 20.
| Number | 398 |
| Square root (decimal) | 19.949937 |
| Simplified radical | √398 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 398
398 = 2 × 199. This is what determines the simplified radical: for √398 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √398 is already in simplest radical form as √398.
Estimating √398 by hand
√398 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 398 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.973684 |
| Step 2 | 19.949951 |
| Step 3 | 19.949937 |
After 3 steps the estimate is 19.949937, matching √398 ≈ 19.949937.
Nearby square roots
Frequently asked questions
Is 398 a perfect square?
No, 398 is not a perfect square, so its square root is irrational and approximately 19.949937.
What is the square root of 398 in simplest radical form?
√398 = √398 in simplest radical form.