Square Root Calculator › Square root of 50
Square Root of 50
√50 ≈ 7.071068
50 is not a perfect square, so √50 is an irrational number that is approximately 7.071068. In simplified radical form, √50 = 5√2.
√50 lies between √49 = 7 and √64 = 8.
| Number | 50 |
| Square root (decimal) | 7.071068 |
| Simplified radical | 5√2 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 50
50 = 2 × 5^2. This is what determines the simplified radical: for √50 you pull out one copy of any prime that appears twice.
Here the paired factor 5 comes out from under the root, leaving √50 = 5√2.
Estimating √50 by hand
√50 falls between √49 = 7 and √64 = 8, so it starts at 7.something. The Babylonian method refines that guess by averaging it with 50 ÷ the guess:
| Step | Estimate |
| Start | 7 |
| Step 1 | 7.071429 |
| Step 2 | 7.071068 |
| Step 3 | 7.071068 |
After 3 steps the estimate is 7.071068, matching √50 ≈ 7.071068.
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Frequently asked questions
Is 50 a perfect square?
No, 50 is not a perfect square, so its square root is irrational and approximately 7.071068.
What is the square root of 50 in simplest radical form?
√50 = 5√2 in simplest radical form.