Square Root Calculator › Square root of 320
Square Root of 320
√320 ≈ 17.888544
320 is not a perfect square, so √320 is an irrational number that is approximately 17.888544. In simplified radical form, √320 = 8√5.
√320 lies between √289 = 17 and √324 = 18.
| Number | 320 |
| Square root (decimal) | 17.888544 |
| Simplified radical | 8√5 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 320
320 = 2^6 × 5. This is what determines the simplified radical: for √320 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √320 = 8√5.
Estimating √320 by hand
√320 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 320 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.911765 |
| Step 2 | 17.888559 |
| Step 3 | 17.888544 |
After 3 steps the estimate is 17.888544, matching √320 ≈ 17.888544.
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Frequently asked questions
Is 320 a perfect square?
No, 320 is not a perfect square, so its square root is irrational and approximately 17.888544.
What is the square root of 320 in simplest radical form?
√320 = 8√5 in simplest radical form.