Square Root Calculator › Square root of 151
Square Root of 151
√151 ≈ 12.288206
151 is not a perfect square, so √151 is an irrational number that is approximately 12.288206. In simplified radical form, √151 = √151.
√151 lies between √144 = 12 and √169 = 13.
| Number | 151 |
| Square root (decimal) | 12.288206 |
| Simplified radical | √151 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 151
151 = 151. This is what determines the simplified radical: for √151 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √151 is already in simplest radical form as √151.
Estimating √151 by hand
√151 falls between √144 = 12 and √169 = 13, so it starts at 12.something. The Babylonian method refines that guess by averaging it with 151 ÷ the guess:
| Step | Estimate |
| Start | 12 |
| Step 1 | 12.291667 |
| Step 2 | 12.288206 |
| Step 3 | 12.288206 |
After 3 steps the estimate is 12.288206, matching √151 ≈ 12.288206.
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Frequently asked questions
Is 151 a perfect square?
No, 151 is not a perfect square, so its square root is irrational and approximately 12.288206.
What is the square root of 151 in simplest radical form?
√151 = √151 in simplest radical form.