Square Root Calculator › Square root of 203
Square Root of 203
√203 ≈ 14.247807
203 is not a perfect square, so √203 is an irrational number that is approximately 14.247807. In simplified radical form, √203 = √203.
√203 lies between √196 = 14 and √225 = 15.
| Number | 203 |
| Square root (decimal) | 14.247807 |
| Simplified radical | √203 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 203
203 = 7 × 29. This is what determines the simplified radical: for √203 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √203 is already in simplest radical form as √203.
Estimating √203 by hand
√203 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 203 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.25 |
| Step 2 | 14.247807 |
| Step 3 | 14.247807 |
After 3 steps the estimate is 14.247807, matching √203 ≈ 14.247807.
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Frequently asked questions
Is 203 a perfect square?
No, 203 is not a perfect square, so its square root is irrational and approximately 14.247807.
What is the square root of 203 in simplest radical form?
√203 = √203 in simplest radical form.