Square root of 409
The square root of 409 is 20.223748 (rounded to 6 decimal places). It cannot be simplified.
Square root of 409
Pick any whole number from 1 to 10,000.
How to work it out
- 1
The square root of 409 is the number that multiplied by itself gives 409.
- 2
409 is between the perfect squares 20² = 400 and 21² = 441, so its square root is between 20 and 21.
- 3
409 has no square factor bigger than 1, so the radical stays as it is.
- 4
A calculator, or long division of digits, gives
LaTeX source of the formulas on this page
\[ \sqrt{409} = \sqrt{409} \approx 20.223748 \]
\[ \sqrt{409} \]
\[ \sqrt{409} \approx 20.223748 \]Squares around 409
| Number | Squared |
|---|---|
| 19 | 361 |
| 20 | 400 |
| 21 | 441 |
| 22 | 484 |
Questions
What is the square root of 409?
The square root of 409 is 20.223748 (rounded to 6 decimal places). It cannot be simplified.
Is 409 a perfect square?
No. It lies between 20² = 400 and 21² = 441.
What is 409 squared?
409 × 409 = 167281.
What is the square root of 409 rounded to 2 decimals?
20.22.