Square Root Calculator › Square root of 43
Square Root of 43
√43 ≈ 6.557439
43 is not a perfect square, so √43 is an irrational number that is approximately 6.557439. In simplified radical form, √43 = √43.
√43 lies between √36 = 6 and √49 = 7.
| Number | 43 |
| Square root (decimal) | 6.557439 |
| Simplified radical | √43 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 43
43 = 43. This is what determines the simplified radical: for √43 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √43 is already in simplest radical form as √43.
Estimating √43 by hand
√43 falls between √36 = 6 and √49 = 7, so it starts at 6.something. The Babylonian method refines that guess by averaging it with 43 ÷ the guess:
| Step | Estimate |
| Start | 6 |
| Step 1 | 6.583333 |
| Step 2 | 6.557489 |
| Step 3 | 6.557439 |
After 3 steps the estimate is 6.557439, matching √43 ≈ 6.557439.
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Frequently asked questions
Is 43 a perfect square?
No, 43 is not a perfect square, so its square root is irrational and approximately 6.557439.
What is the square root of 43 in simplest radical form?
√43 = √43 in simplest radical form.