Square Root Calculator › Square root of 452
Square Root of 452
√452 ≈ 21.260292
452 is not a perfect square, so √452 is an irrational number that is approximately 21.260292. In simplified radical form, √452 = 2√113.
√452 lies between √441 = 21 and √484 = 22.
| Number | 452 |
| Square root (decimal) | 21.260292 |
| Simplified radical | 2√113 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 452
452 = 2^2 × 113. This is what determines the simplified radical: for √452 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √452 = 2√113.
Estimating √452 by hand
√452 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 452 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.261905 |
| Step 2 | 21.260292 |
| Step 3 | 21.260292 |
After 3 steps the estimate is 21.260292, matching √452 ≈ 21.260292.
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Frequently asked questions
Is 452 a perfect square?
No, 452 is not a perfect square, so its square root is irrational and approximately 21.260292.
What is the square root of 452 in simplest radical form?
√452 = 2√113 in simplest radical form.