Square Root Calculator › Square root of 47
Square Root of 47
√47 ≈ 6.855655
47 is not a perfect square, so √47 is an irrational number that is approximately 6.855655. In simplified radical form, √47 = √47.
√47 lies between √36 = 6 and √49 = 7.
| Number | 47 |
| Square root (decimal) | 6.855655 |
| Simplified radical | √47 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 47
47 = 47. This is what determines the simplified radical: for √47 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √47 is already in simplest radical form as √47.
Estimating √47 by hand
√47 falls between √36 = 6 and √49 = 7, so it starts at 6.something. The Babylonian method refines that guess by averaging it with 47 ÷ the guess:
| Step | Estimate |
| Start | 6 |
| Step 1 | 6.916667 |
| Step 2 | 6.855924 |
| Step 3 | 6.855655 |
After 3 steps the estimate is 6.855655, matching √47 ≈ 6.855655.
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Frequently asked questions
Is 47 a perfect square?
No, 47 is not a perfect square, so its square root is irrational and approximately 6.855655.
What is the square root of 47 in simplest radical form?
√47 = √47 in simplest radical form.