Square Root Calculator › Square root of 425
Square Root of 425
√425 ≈ 20.615528
425 is not a perfect square, so √425 is an irrational number that is approximately 20.615528. In simplified radical form, √425 = 5√17.
√425 lies between √400 = 20 and √441 = 21.
| Number | 425 |
| Square root (decimal) | 20.615528 |
| Simplified radical | 5√17 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 425
425 = 5^2 × 17. This is what determines the simplified radical: for √425 you pull out one copy of any prime that appears twice.
Here the paired factor 5 comes out from under the root, leaving √425 = 5√17.
Estimating √425 by hand
√425 falls between √400 = 20 and √441 = 21, so it starts at 20.something. The Babylonian method refines that guess by averaging it with 425 ÷ the guess:
| Step | Estimate |
| Start | 20 |
| Step 1 | 20.625 |
| Step 2 | 20.61553 |
| Step 3 | 20.615528 |
After 3 steps the estimate is 20.615528, matching √425 ≈ 20.615528.
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Frequently asked questions
Is 425 a perfect square?
No, 425 is not a perfect square, so its square root is irrational and approximately 20.615528.
What is the square root of 425 in simplest radical form?
√425 = 5√17 in simplest radical form.