Square Root Calculator › Square root of 71
Square Root of 71
√71 ≈ 8.42615
71 is not a perfect square, so √71 is an irrational number that is approximately 8.42615. In simplified radical form, √71 = √71.
√71 lies between √64 = 8 and √81 = 9.
| Number | 71 |
| Square root (decimal) | 8.42615 |
| Simplified radical | √71 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 71
71 = 71. This is what determines the simplified radical: for √71 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √71 is already in simplest radical form as √71.
Estimating √71 by hand
√71 falls between √64 = 8 and √81 = 9, so it starts at 8.something. The Babylonian method refines that guess by averaging it with 71 ÷ the guess:
| Step | Estimate |
| Start | 8 |
| Step 1 | 8.4375 |
| Step 2 | 8.426157 |
| Step 3 | 8.42615 |
After 3 steps the estimate is 8.42615, matching √71 ≈ 8.42615.
Nearby square roots
Frequently asked questions
Is 71 a perfect square?
No, 71 is not a perfect square, so its square root is irrational and approximately 8.42615.
What is the square root of 71 in simplest radical form?
√71 = √71 in simplest radical form.