Square Root Calculator › Square root of 438
Square Root of 438
√438 ≈ 20.92845
438 is not a perfect square, so √438 is an irrational number that is approximately 20.92845. In simplified radical form, √438 = √438.
√438 lies between √400 = 20 and √441 = 21.
| Number | 438 |
| Square root (decimal) | 20.92845 |
| Simplified radical | √438 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 438
438 = 2 × 3 × 73. This is what determines the simplified radical: for √438 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √438 is already in simplest radical form as √438.
Estimating √438 by hand
√438 falls between √400 = 20 and √441 = 21, so it starts at 20.something. The Babylonian method refines that guess by averaging it with 438 ÷ the guess:
| Step | Estimate |
| Start | 20 |
| Step 1 | 20.95 |
| Step 2 | 20.928461 |
| Step 3 | 20.92845 |
After 3 steps the estimate is 20.92845, matching √438 ≈ 20.92845.
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Frequently asked questions
Is 438 a perfect square?
No, 438 is not a perfect square, so its square root is irrational and approximately 20.92845.
What is the square root of 438 in simplest radical form?
√438 = √438 in simplest radical form.