Square Root Calculator › Square root of 18
Square Root of 18
√18 ≈ 4.242641
18 is not a perfect square, so √18 is an irrational number that is approximately 4.242641. In simplified radical form, √18 = 3√2.
√18 lies between √16 = 4 and √25 = 5.
| Number | 18 |
| Square root (decimal) | 4.242641 |
| Simplified radical | 3√2 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 18
18 = 2 × 3^2. This is what determines the simplified radical: for √18 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √18 = 3√2.
Estimating √18 by hand
√18 falls between √16 = 4 and √25 = 5, so it starts at 4.something. The Babylonian method refines that guess by averaging it with 18 ÷ the guess:
| Step | Estimate |
| Start | 4 |
| Step 1 | 4.25 |
| Step 2 | 4.242647 |
| Step 3 | 4.242641 |
After 3 steps the estimate is 4.242641, matching √18 ≈ 4.242641.
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Frequently asked questions
Is 18 a perfect square?
No, 18 is not a perfect square, so its square root is irrational and approximately 4.242641.
What is the square root of 18 in simplest radical form?
√18 = 3√2 in simplest radical form.