Square Root Calculator › Square root of 342
Square Root of 342
√342 ≈ 18.493242
342 is not a perfect square, so √342 is an irrational number that is approximately 18.493242. In simplified radical form, √342 = 3√38.
√342 lies between √324 = 18 and √361 = 19.
| Number | 342 |
| Square root (decimal) | 18.493242 |
| Simplified radical | 3√38 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 342
342 = 2 × 3^2 × 19. This is what determines the simplified radical: for √342 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √342 = 3√38.
Estimating √342 by hand
√342 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 342 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.5 |
| Step 2 | 18.493243 |
| Step 3 | 18.493242 |
After 3 steps the estimate is 18.493242, matching √342 ≈ 18.493242.
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Frequently asked questions
Is 342 a perfect square?
No, 342 is not a perfect square, so its square root is irrational and approximately 18.493242.
What is the square root of 342 in simplest radical form?
√342 = 3√38 in simplest radical form.