Square Root Calculator › Square root of 188
Square Root of 188
√188 ≈ 13.711309
188 is not a perfect square, so √188 is an irrational number that is approximately 13.711309. In simplified radical form, √188 = 2√47.
√188 lies between √169 = 13 and √196 = 14.
| Number | 188 |
| Square root (decimal) | 13.711309 |
| Simplified radical | 2√47 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 188
188 = 2^2 × 47. This is what determines the simplified radical: for √188 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √188 = 2√47.
Estimating √188 by hand
√188 falls between √169 = 13 and √196 = 14, so it starts at 13.something. The Babylonian method refines that guess by averaging it with 188 ÷ the guess:
| Step | Estimate |
| Start | 13 |
| Step 1 | 13.730769 |
| Step 2 | 13.711323 |
| Step 3 | 13.711309 |
After 3 steps the estimate is 13.711309, matching √188 ≈ 13.711309.
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Frequently asked questions
Is 188 a perfect square?
No, 188 is not a perfect square, so its square root is irrational and approximately 13.711309.
What is the square root of 188 in simplest radical form?
√188 = 2√47 in simplest radical form.