Square Root Calculator › Square root of 242
Square Root of 242
√242 ≈ 15.556349
242 is not a perfect square, so √242 is an irrational number that is approximately 15.556349. In simplified radical form, √242 = 11√2.
√242 lies between √225 = 15 and √256 = 16.
| Number | 242 |
| Square root (decimal) | 15.556349 |
| Simplified radical | 11√2 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 242
242 = 2 × 11^2. This is what determines the simplified radical: for √242 you pull out one copy of any prime that appears twice.
Here the paired factor 11 comes out from under the root, leaving √242 = 11√2.
Estimating √242 by hand
√242 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 242 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.566667 |
| Step 2 | 15.556353 |
| Step 3 | 15.556349 |
After 3 steps the estimate is 15.556349, matching √242 ≈ 15.556349.
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Frequently asked questions
Is 242 a perfect square?
No, 242 is not a perfect square, so its square root is irrational and approximately 15.556349.
What is the square root of 242 in simplest radical form?
√242 = 11√2 in simplest radical form.