Square Root Calculator › Square root of 20
Square Root of 20
√20 ≈ 4.472136
20 is not a perfect square, so √20 is an irrational number that is approximately 4.472136. In simplified radical form, √20 = 2√5.
√20 lies between √16 = 4 and √25 = 5.
| Number | 20 |
| Square root (decimal) | 4.472136 |
| Simplified radical | 2√5 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 20
20 = 2^2 × 5. This is what determines the simplified radical: for √20 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √20 = 2√5.
Estimating √20 by hand
√20 falls between √16 = 4 and √25 = 5, so it starts at 4.something. The Babylonian method refines that guess by averaging it with 20 ÷ the guess:
| Step | Estimate |
| Start | 4 |
| Step 1 | 4.5 |
| Step 2 | 4.472222 |
| Step 3 | 4.472136 |
After 3 steps the estimate is 4.472136, matching √20 ≈ 4.472136.
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Frequently asked questions
Is 20 a perfect square?
No, 20 is not a perfect square, so its square root is irrational and approximately 4.472136.
What is the square root of 20 in simplest radical form?
√20 = 2√5 in simplest radical form.