Square Root Calculator › Square root of 375
Square Root of 375
√375 ≈ 19.364917
375 is not a perfect square, so √375 is an irrational number that is approximately 19.364917. In simplified radical form, √375 = 5√15.
√375 lies between √361 = 19 and √400 = 20.
| Number | 375 |
| Square root (decimal) | 19.364917 |
| Simplified radical | 5√15 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 375
375 = 3 × 5^3. This is what determines the simplified radical: for √375 you pull out one copy of any prime that appears twice.
Here the paired factor 5 comes out from under the root, leaving √375 = 5√15.
Estimating √375 by hand
√375 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 375 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.368421 |
| Step 2 | 19.364917 |
| Step 3 | 19.364917 |
After 3 steps the estimate is 19.364917, matching √375 ≈ 19.364917.
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Frequently asked questions
Is 375 a perfect square?
No, 375 is not a perfect square, so its square root is irrational and approximately 19.364917.
What is the square root of 375 in simplest radical form?
√375 = 5√15 in simplest radical form.