Square Root Calculator › Square root of 445
Square Root of 445
√445 ≈ 21.095023
445 is not a perfect square, so √445 is an irrational number that is approximately 21.095023. In simplified radical form, √445 = √445.
√445 lies between √441 = 21 and √484 = 22.
| Number | 445 |
| Square root (decimal) | 21.095023 |
| Simplified radical | √445 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 445
445 = 5 × 89. This is what determines the simplified radical: for √445 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √445 is already in simplest radical form as √445.
Estimating √445 by hand
√445 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 445 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.095238 |
| Step 2 | 21.095023 |
| Step 3 | 21.095023 |
After 3 steps the estimate is 21.095023, matching √445 ≈ 21.095023.
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Frequently asked questions
Is 445 a perfect square?
No, 445 is not a perfect square, so its square root is irrational and approximately 21.095023.
What is the square root of 445 in simplest radical form?
√445 = √445 in simplest radical form.