Square Root Calculator › Square root of 7
Square Root of 7
√7 ≈ 2.645751
7 is not a perfect square, so √7 is an irrational number that is approximately 2.645751. In simplified radical form, √7 = √7.
√7 lies between √4 = 2 and √9 = 3.
| Number | 7 |
| Square root (decimal) | 2.645751 |
| Simplified radical | √7 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 7
7 = 7. This is what determines the simplified radical: for √7 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √7 is already in simplest radical form as √7.
Estimating √7 by hand
√7 falls between √4 = 2 and √9 = 3, so it starts at 2.something. The Babylonian method refines that guess by averaging it with 7 ÷ the guess:
| Step | Estimate |
| Start | 2 |
| Step 1 | 2.75 |
| Step 2 | 2.647727 |
| Step 3 | 2.645752 |
After 3 steps the estimate is 2.645752, matching √7 ≈ 2.645751.
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Frequently asked questions
Is 7 a perfect square?
No, 7 is not a perfect square, so its square root is irrational and approximately 2.645751.
What is the square root of 7 in simplest radical form?
√7 = √7 in simplest radical form.