Square Root Calculator › Square root of 450
Square Root of 450
√450 ≈ 21.213203
450 is not a perfect square, so √450 is an irrational number that is approximately 21.213203. In simplified radical form, √450 = 15√2.
√450 lies between √441 = 21 and √484 = 22.
| Number | 450 |
| Square root (decimal) | 21.213203 |
| Simplified radical | 15√2 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 450
450 = 2 × 3^2 × 5^2. This is what determines the simplified radical: for √450 you pull out one copy of any prime that appears twice.
Here the paired factors 3 and 5 come out from under the root, leaving √450 = 15√2.
Estimating √450 by hand
√450 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 450 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.214286 |
| Step 2 | 21.213203 |
| Step 3 | 21.213203 |
After 3 steps the estimate is 21.213203, matching √450 ≈ 21.213203.
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Frequently asked questions
Is 450 a perfect square?
No, 450 is not a perfect square, so its square root is irrational and approximately 21.213203.
What is the square root of 450 in simplest radical form?
√450 = 15√2 in simplest radical form.