Square Root Calculator › Square root of 74
Square Root of 74
√74 ≈ 8.602325
74 is not a perfect square, so √74 is an irrational number that is approximately 8.602325. In simplified radical form, √74 = √74.
√74 lies between √64 = 8 and √81 = 9.
| Number | 74 |
| Square root (decimal) | 8.602325 |
| Simplified radical | √74 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 74
74 = 2 × 37. This is what determines the simplified radical: for √74 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √74 is already in simplest radical form as √74.
Estimating √74 by hand
√74 falls between √64 = 8 and √81 = 9, so it starts at 8.something. The Babylonian method refines that guess by averaging it with 74 ÷ the guess:
| Step | Estimate |
| Start | 8 |
| Step 1 | 8.625 |
| Step 2 | 8.602355 |
| Step 3 | 8.602325 |
After 3 steps the estimate is 8.602325, matching √74 ≈ 8.602325.
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Frequently asked questions
Is 74 a perfect square?
No, 74 is not a perfect square, so its square root is irrational and approximately 8.602325.
What is the square root of 74 in simplest radical form?
√74 = √74 in simplest radical form.