Square Root Calculator › Square root of 24
Square Root of 24
√24 ≈ 4.898979
24 is not a perfect square, so √24 is an irrational number that is approximately 4.898979. In simplified radical form, √24 = 2√6.
√24 lies between √16 = 4 and √25 = 5.
| Number | 24 |
| Square root (decimal) | 4.898979 |
| Simplified radical | 2√6 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 24
24 = 2^3 × 3. This is what determines the simplified radical: for √24 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √24 = 2√6.
Estimating √24 by hand
√24 falls between √16 = 4 and √25 = 5, so it starts at 4.something. The Babylonian method refines that guess by averaging it with 24 ÷ the guess:
| Step | Estimate |
| Start | 4 |
| Step 1 | 5 |
| Step 2 | 4.9 |
| Step 3 | 4.89898 |
After 3 steps the estimate is 4.89898, matching √24 ≈ 4.898979.
Nearby square roots
Frequently asked questions
Is 24 a perfect square?
No, 24 is not a perfect square, so its square root is irrational and approximately 4.898979.
What is the square root of 24 in simplest radical form?
√24 = 2√6 in simplest radical form.