Square Root Calculator › Square root of 15
Square Root of 15
√15 ≈ 3.872983
15 is not a perfect square, so √15 is an irrational number that is approximately 3.872983. In simplified radical form, √15 = √15.
√15 lies between √9 = 3 and √16 = 4.
| Number | 15 |
| Square root (decimal) | 3.872983 |
| Simplified radical | √15 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 15
15 = 3 × 5. This is what determines the simplified radical: for √15 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √15 is already in simplest radical form as √15.
Estimating √15 by hand
√15 falls between √9 = 3 and √16 = 4, so it starts at 3.something. The Babylonian method refines that guess by averaging it with 15 ÷ the guess:
| Step | Estimate |
| Start | 3 |
| Step 1 | 4 |
| Step 2 | 3.875 |
| Step 3 | 3.872984 |
After 3 steps the estimate is 3.872984, matching √15 ≈ 3.872983.
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Frequently asked questions
Is 15 a perfect square?
No, 15 is not a perfect square, so its square root is irrational and approximately 3.872983.
What is the square root of 15 in simplest radical form?
√15 = √15 in simplest radical form.