Square Root Calculator › Square root of 148
Square Root of 148
√148 ≈ 12.165525
148 is not a perfect square, so √148 is an irrational number that is approximately 12.165525. In simplified radical form, √148 = 2√37.
√148 lies between √144 = 12 and √169 = 13.
| Number | 148 |
| Square root (decimal) | 12.165525 |
| Simplified radical | 2√37 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 148
148 = 2^2 × 37. This is what determines the simplified radical: for √148 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √148 = 2√37.
Estimating √148 by hand
√148 falls between √144 = 12 and √169 = 13, so it starts at 12.something. The Babylonian method refines that guess by averaging it with 148 ÷ the guess:
| Step | Estimate |
| Start | 12 |
| Step 1 | 12.166667 |
| Step 2 | 12.165525 |
| Step 3 | 12.165525 |
After 3 steps the estimate is 12.165525, matching √148 ≈ 12.165525.
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Frequently asked questions
Is 148 a perfect square?
No, 148 is not a perfect square, so its square root is irrational and approximately 12.165525.
What is the square root of 148 in simplest radical form?
√148 = 2√37 in simplest radical form.