Square Root Calculator › Square root of 53
Square Root of 53
√53 ≈ 7.28011
53 is not a perfect square, so √53 is an irrational number that is approximately 7.28011. In simplified radical form, √53 = √53.
√53 lies between √49 = 7 and √64 = 8.
| Number | 53 |
| Square root (decimal) | 7.28011 |
| Simplified radical | √53 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 53
53 = 53. This is what determines the simplified radical: for √53 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √53 is already in simplest radical form as √53.
Estimating √53 by hand
√53 falls between √49 = 7 and √64 = 8, so it starts at 7.something. The Babylonian method refines that guess by averaging it with 53 ÷ the guess:
| Step | Estimate |
| Start | 7 |
| Step 1 | 7.285714 |
| Step 2 | 7.280112 |
| Step 3 | 7.28011 |
After 3 steps the estimate is 7.28011, matching √53 ≈ 7.28011.
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Frequently asked questions
Is 53 a perfect square?
No, 53 is not a perfect square, so its square root is irrational and approximately 7.28011.
What is the square root of 53 in simplest radical form?
√53 = √53 in simplest radical form.