Square Root Calculator › Square root of 336
Square Root of 336
√336 ≈ 18.330303
336 is not a perfect square, so √336 is an irrational number that is approximately 18.330303. In simplified radical form, √336 = 4√21.
√336 lies between √324 = 18 and √361 = 19.
| Number | 336 |
| Square root (decimal) | 18.330303 |
| Simplified radical | 4√21 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 336
336 = 2^4 × 3 × 7. This is what determines the simplified radical: for √336 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √336 = 4√21.
Estimating √336 by hand
√336 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 336 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.333333 |
| Step 2 | 18.330303 |
| Step 3 | 18.330303 |
After 3 steps the estimate is 18.330303, matching √336 ≈ 18.330303.
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Frequently asked questions
Is 336 a perfect square?
No, 336 is not a perfect square, so its square root is irrational and approximately 18.330303.
What is the square root of 336 in simplest radical form?
√336 = 4√21 in simplest radical form.