Square Root Calculator › Square root of 13
Square Root of 13
√13 ≈ 3.605551
13 is not a perfect square, so √13 is an irrational number that is approximately 3.605551. In simplified radical form, √13 = √13.
√13 lies between √9 = 3 and √16 = 4.
| Number | 13 |
| Square root (decimal) | 3.605551 |
| Simplified radical | √13 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 13
13 = 13. This is what determines the simplified radical: for √13 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √13 is already in simplest radical form as √13.
Estimating √13 by hand
√13 falls between √9 = 3 and √16 = 4, so it starts at 3.something. The Babylonian method refines that guess by averaging it with 13 ÷ the guess:
| Step | Estimate |
| Start | 3 |
| Step 1 | 3.666667 |
| Step 2 | 3.606061 |
| Step 3 | 3.605551 |
After 3 steps the estimate is 3.605551, matching √13 ≈ 3.605551.
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Frequently asked questions
Is 13 a perfect square?
No, 13 is not a perfect square, so its square root is irrational and approximately 3.605551.
What is the square root of 13 in simplest radical form?
√13 = √13 in simplest radical form.