Square Root Calculator › Square root of 73
Square Root of 73
√73 ≈ 8.544004
73 is not a perfect square, so √73 is an irrational number that is approximately 8.544004. In simplified radical form, √73 = √73.
√73 lies between √64 = 8 and √81 = 9.
| Number | 73 |
| Square root (decimal) | 8.544004 |
| Simplified radical | √73 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 73
73 = 73. This is what determines the simplified radical: for √73 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √73 is already in simplest radical form as √73.
Estimating √73 by hand
√73 falls between √64 = 8 and √81 = 9, so it starts at 8.something. The Babylonian method refines that guess by averaging it with 73 ÷ the guess:
| Step | Estimate |
| Start | 8 |
| Step 1 | 8.5625 |
| Step 2 | 8.544024 |
| Step 3 | 8.544004 |
After 3 steps the estimate is 8.544004, matching √73 ≈ 8.544004.
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Frequently asked questions
Is 73 a perfect square?
No, 73 is not a perfect square, so its square root is irrational and approximately 8.544004.
What is the square root of 73 in simplest radical form?
√73 = √73 in simplest radical form.