Square Root Calculator › Square root of 62
Square Root of 62
√62 ≈ 7.874008
62 is not a perfect square, so √62 is an irrational number that is approximately 7.874008. In simplified radical form, √62 = √62.
√62 lies between √49 = 7 and √64 = 8.
| Number | 62 |
| Square root (decimal) | 7.874008 |
| Simplified radical | √62 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 62
62 = 2 × 31. This is what determines the simplified radical: for √62 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √62 is already in simplest radical form as √62.
Estimating √62 by hand
√62 falls between √49 = 7 and √64 = 8, so it starts at 7.something. The Babylonian method refines that guess by averaging it with 62 ÷ the guess:
| Step | Estimate |
| Start | 7 |
| Step 1 | 7.928571 |
| Step 2 | 7.874196 |
| Step 3 | 7.874008 |
After 3 steps the estimate is 7.874008, matching √62 ≈ 7.874008.
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Frequently asked questions
Is 62 a perfect square?
No, 62 is not a perfect square, so its square root is irrational and approximately 7.874008.
What is the square root of 62 in simplest radical form?
√62 = √62 in simplest radical form.