Square Root Calculator › Square root of 202
Square Root of 202
√202 ≈ 14.21267
202 is not a perfect square, so √202 is an irrational number that is approximately 14.21267. In simplified radical form, √202 = √202.
√202 lies between √196 = 14 and √225 = 15.
| Number | 202 |
| Square root (decimal) | 14.21267 |
| Simplified radical | √202 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 202
202 = 2 × 101. This is what determines the simplified radical: for √202 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √202 is already in simplest radical form as √202.
Estimating √202 by hand
√202 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 202 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.214286 |
| Step 2 | 14.21267 |
| Step 3 | 14.21267 |
After 3 steps the estimate is 14.21267, matching √202 ≈ 14.21267.
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Frequently asked questions
Is 202 a perfect square?
No, 202 is not a perfect square, so its square root is irrational and approximately 14.21267.
What is the square root of 202 in simplest radical form?
√202 = √202 in simplest radical form.