Square Root Calculator › Square root of 130
Square Root of 130
√130 ≈ 11.401754
130 is not a perfect square, so √130 is an irrational number that is approximately 11.401754. In simplified radical form, √130 = √130.
√130 lies between √121 = 11 and √144 = 12.
| Number | 130 |
| Square root (decimal) | 11.401754 |
| Simplified radical | √130 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 130
130 = 2 × 5 × 13. This is what determines the simplified radical: for √130 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √130 is already in simplest radical form as √130.
Estimating √130 by hand
√130 falls between √121 = 11 and √144 = 12, so it starts at 11.something. The Babylonian method refines that guess by averaging it with 130 ÷ the guess:
| Step | Estimate |
| Start | 11 |
| Step 1 | 11.409091 |
| Step 2 | 11.401757 |
| Step 3 | 11.401754 |
After 3 steps the estimate is 11.401754, matching √130 ≈ 11.401754.
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Frequently asked questions
Is 130 a perfect square?
No, 130 is not a perfect square, so its square root is irrational and approximately 11.401754.
What is the square root of 130 in simplest radical form?
√130 = √130 in simplest radical form.