Square Root Calculator › Square root of 40
Square Root of 40
√40 ≈ 6.324555
40 is not a perfect square, so √40 is an irrational number that is approximately 6.324555. In simplified radical form, √40 = 2√10.
√40 lies between √36 = 6 and √49 = 7.
| Number | 40 |
| Square root (decimal) | 6.324555 |
| Simplified radical | 2√10 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 40
40 = 2^3 × 5. This is what determines the simplified radical: for √40 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √40 = 2√10.
Estimating √40 by hand
√40 falls between √36 = 6 and √49 = 7, so it starts at 6.something. The Babylonian method refines that guess by averaging it with 40 ÷ the guess:
| Step | Estimate |
| Start | 6 |
| Step 1 | 6.333333 |
| Step 2 | 6.324561 |
| Step 3 | 6.324555 |
After 3 steps the estimate is 6.324555, matching √40 ≈ 6.324555.
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Frequently asked questions
Is 40 a perfect square?
No, 40 is not a perfect square, so its square root is irrational and approximately 6.324555.
What is the square root of 40 in simplest radical form?
√40 = 2√10 in simplest radical form.