Square Root Calculator › Square root of 155
Square Root of 155
√155 ≈ 12.4499
155 is not a perfect square, so √155 is an irrational number that is approximately 12.4499. In simplified radical form, √155 = √155.
√155 lies between √144 = 12 and √169 = 13.
| Number | 155 |
| Square root (decimal) | 12.4499 |
| Simplified radical | √155 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 155
155 = 5 × 31. This is what determines the simplified radical: for √155 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √155 is already in simplest radical form as √155.
Estimating √155 by hand
√155 falls between √144 = 12 and √169 = 13, so it starts at 12.something. The Babylonian method refines that guess by averaging it with 155 ÷ the guess:
| Step | Estimate |
| Start | 12 |
| Step 1 | 12.458333 |
| Step 2 | 12.449902 |
| Step 3 | 12.4499 |
After 3 steps the estimate is 12.4499, matching √155 ≈ 12.4499.
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Frequently asked questions
Is 155 a perfect square?
No, 155 is not a perfect square, so its square root is irrational and approximately 12.4499.
What is the square root of 155 in simplest radical form?
√155 = √155 in simplest radical form.