Square Root Calculator › Square root of 22
Square Root of 22
√22 ≈ 4.690416
22 is not a perfect square, so √22 is an irrational number that is approximately 4.690416. In simplified radical form, √22 = √22.
√22 lies between √16 = 4 and √25 = 5.
| Number | 22 |
| Square root (decimal) | 4.690416 |
| Simplified radical | √22 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 22
22 = 2 × 11. This is what determines the simplified radical: for √22 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √22 is already in simplest radical form as √22.
Estimating √22 by hand
√22 falls between √16 = 4 and √25 = 5, so it starts at 4.something. The Babylonian method refines that guess by averaging it with 22 ÷ the guess:
| Step | Estimate |
| Start | 4 |
| Step 1 | 4.75 |
| Step 2 | 4.690789 |
| Step 3 | 4.690416 |
After 3 steps the estimate is 4.690416, matching √22 ≈ 4.690416.
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Frequently asked questions
Is 22 a perfect square?
No, 22 is not a perfect square, so its square root is irrational and approximately 4.690416.
What is the square root of 22 in simplest radical form?
√22 = √22 in simplest radical form.