Square Root Calculator › Square root of 224
Square Root of 224
√224 ≈ 14.96663
224 is not a perfect square, so √224 is an irrational number that is approximately 14.96663. In simplified radical form, √224 = 4√14.
√224 lies between √196 = 14 and √225 = 15.
| Number | 224 |
| Square root (decimal) | 14.96663 |
| Simplified radical | 4√14 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 224
224 = 2^5 × 7. This is what determines the simplified radical: for √224 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √224 = 4√14.
Estimating √224 by hand
√224 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 224 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 15 |
| Step 2 | 14.966667 |
| Step 3 | 14.96663 |
After 3 steps the estimate is 14.96663, matching √224 ≈ 14.96663.
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Frequently asked questions
Is 224 a perfect square?
No, 224 is not a perfect square, so its square root is irrational and approximately 14.96663.
What is the square root of 224 in simplest radical form?
√224 = 4√14 in simplest radical form.