Square Root Calculator › Square root of 200
Square Root of 200
√200 ≈ 14.142136
200 is not a perfect square, so √200 is an irrational number that is approximately 14.142136. In simplified radical form, √200 = 10√2.
√200 lies between √196 = 14 and √225 = 15.
| Number | 200 |
| Square root (decimal) | 14.142136 |
| Simplified radical | 10√2 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 200
200 = 2^3 × 5^2. This is what determines the simplified radical: for √200 you pull out one copy of any prime that appears twice.
Here the paired factors 2 and 5 come out from under the root, leaving √200 = 10√2.
Estimating √200 by hand
√200 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 200 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.142857 |
| Step 2 | 14.142136 |
| Step 3 | 14.142136 |
After 3 steps the estimate is 14.142136, matching √200 ≈ 14.142136.
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Frequently asked questions
Is 200 a perfect square?
No, 200 is not a perfect square, so its square root is irrational and approximately 14.142136.
What is the square root of 200 in simplest radical form?
√200 = 10√2 in simplest radical form.