Square Root Calculator › Square root of 243
Square Root of 243
√243 ≈ 15.588457
243 is not a perfect square, so √243 is an irrational number that is approximately 15.588457. In simplified radical form, √243 = 9√3.
√243 lies between √225 = 15 and √256 = 16.
| Number | 243 |
| Square root (decimal) | 15.588457 |
| Simplified radical | 9√3 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 243
243 = 3^5. This is what determines the simplified radical: for √243 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √243 = 9√3.
Estimating √243 by hand
√243 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 243 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.6 |
| Step 2 | 15.588462 |
| Step 3 | 15.588457 |
After 3 steps the estimate is 15.588457, matching √243 ≈ 15.588457.
Nearby square roots
Frequently asked questions
Is 243 a perfect square?
No, 243 is not a perfect square, so its square root is irrational and approximately 15.588457.
What is the square root of 243 in simplest radical form?
√243 = 9√3 in simplest radical form.