Square Root Calculator › Square root of 63
Square Root of 63
√63 ≈ 7.937254
63 is not a perfect square, so √63 is an irrational number that is approximately 7.937254. In simplified radical form, √63 = 3√7.
√63 lies between √49 = 7 and √64 = 8.
| Number | 63 |
| Square root (decimal) | 7.937254 |
| Simplified radical | 3√7 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 63
63 = 3^2 × 7. This is what determines the simplified radical: for √63 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √63 = 3√7.
Estimating √63 by hand
√63 falls between √49 = 7 and √64 = 8, so it starts at 7.something. The Babylonian method refines that guess by averaging it with 63 ÷ the guess:
| Step | Estimate |
| Start | 7 |
| Step 1 | 8 |
| Step 2 | 7.9375 |
| Step 3 | 7.937254 |
After 3 steps the estimate is 7.937254, matching √63 ≈ 7.937254.
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Frequently asked questions
Is 63 a perfect square?
No, 63 is not a perfect square, so its square root is irrational and approximately 7.937254.
What is the square root of 63 in simplest radical form?
√63 = 3√7 in simplest radical form.