Square Root Calculator › Square root of 210
Square Root of 210
√210 ≈ 14.491377
210 is not a perfect square, so √210 is an irrational number that is approximately 14.491377. In simplified radical form, √210 = √210.
√210 lies between √196 = 14 and √225 = 15.
| Number | 210 |
| Square root (decimal) | 14.491377 |
| Simplified radical | √210 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 210
210 = 2 × 3 × 5 × 7. This is what determines the simplified radical: for √210 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √210 is already in simplest radical form as √210.
Estimating √210 by hand
√210 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 210 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.5 |
| Step 2 | 14.491379 |
| Step 3 | 14.491377 |
After 3 steps the estimate is 14.491377, matching √210 ≈ 14.491377.
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Frequently asked questions
Is 210 a perfect square?
No, 210 is not a perfect square, so its square root is irrational and approximately 14.491377.
What is the square root of 210 in simplest radical form?
√210 = √210 in simplest radical form.