Square Root Calculator › Square root of 56
Square Root of 56
√56 ≈ 7.483315
56 is not a perfect square, so √56 is an irrational number that is approximately 7.483315. In simplified radical form, √56 = 2√14.
√56 lies between √49 = 7 and √64 = 8.
| Number | 56 |
| Square root (decimal) | 7.483315 |
| Simplified radical | 2√14 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 56
56 = 2^3 × 7. This is what determines the simplified radical: for √56 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √56 = 2√14.
Estimating √56 by hand
√56 falls between √49 = 7 and √64 = 8, so it starts at 7.something. The Babylonian method refines that guess by averaging it with 56 ÷ the guess:
| Step | Estimate |
| Start | 7 |
| Step 1 | 7.5 |
| Step 2 | 7.483333 |
| Step 3 | 7.483315 |
After 3 steps the estimate is 7.483315, matching √56 ≈ 7.483315.
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Frequently asked questions
Is 56 a perfect square?
No, 56 is not a perfect square, so its square root is irrational and approximately 7.483315.
What is the square root of 56 in simplest radical form?
√56 = 2√14 in simplest radical form.