Square Root Calculator › Square root of 150
Square Root of 150
√150 ≈ 12.247449
150 is not a perfect square, so √150 is an irrational number that is approximately 12.247449. In simplified radical form, √150 = 5√6.
√150 lies between √144 = 12 and √169 = 13.
| Number | 150 |
| Square root (decimal) | 12.247449 |
| Simplified radical | 5√6 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 150
150 = 2 × 3 × 5^2. This is what determines the simplified radical: for √150 you pull out one copy of any prime that appears twice.
Here the paired factor 5 comes out from under the root, leaving √150 = 5√6.
Estimating √150 by hand
√150 falls between √144 = 12 and √169 = 13, so it starts at 12.something. The Babylonian method refines that guess by averaging it with 150 ÷ the guess:
| Step | Estimate |
| Start | 12 |
| Step 1 | 12.25 |
| Step 2 | 12.247449 |
| Step 3 | 12.247449 |
After 3 steps the estimate is 12.247449, matching √150 ≈ 12.247449.
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Frequently asked questions
Is 150 a perfect square?
No, 150 is not a perfect square, so its square root is irrational and approximately 12.247449.
What is the square root of 150 in simplest radical form?
√150 = 5√6 in simplest radical form.