Square Root Calculator › Square root of 19
Square Root of 19
√19 ≈ 4.358899
19 is not a perfect square, so √19 is an irrational number that is approximately 4.358899. In simplified radical form, √19 = √19.
√19 lies between √16 = 4 and √25 = 5.
| Number | 19 |
| Square root (decimal) | 4.358899 |
| Simplified radical | √19 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 19
19 = 19. This is what determines the simplified radical: for √19 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √19 is already in simplest radical form as √19.
Estimating √19 by hand
√19 falls between √16 = 4 and √25 = 5, so it starts at 4.something. The Babylonian method refines that guess by averaging it with 19 ÷ the guess:
| Step | Estimate |
| Start | 4 |
| Step 1 | 4.375 |
| Step 2 | 4.358929 |
| Step 3 | 4.358899 |
After 3 steps the estimate is 4.358899, matching √19 ≈ 4.358899.
Nearby square roots
Frequently asked questions
Is 19 a perfect square?
No, 19 is not a perfect square, so its square root is irrational and approximately 4.358899.
What is the square root of 19 in simplest radical form?
√19 = √19 in simplest radical form.