Square Root Calculator › Square root of 240
Square Root of 240
√240 ≈ 15.491933
240 is not a perfect square, so √240 is an irrational number that is approximately 15.491933. In simplified radical form, √240 = 4√15.
√240 lies between √225 = 15 and √256 = 16.
| Number | 240 |
| Square root (decimal) | 15.491933 |
| Simplified radical | 4√15 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 240
240 = 2^4 × 3 × 5. This is what determines the simplified radical: for √240 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √240 = 4√15.
Estimating √240 by hand
√240 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 240 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.5 |
| Step 2 | 15.491935 |
| Step 3 | 15.491933 |
After 3 steps the estimate is 15.491933, matching √240 ≈ 15.491933.
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Frequently asked questions
Is 240 a perfect square?
No, 240 is not a perfect square, so its square root is irrational and approximately 15.491933.
What is the square root of 240 in simplest radical form?
√240 = 4√15 in simplest radical form.