Square root of 412

The square root of 412 is 20.297783 (rounded to 6 decimal places). In simplest radical form it is 2√103.

Square root of 412

Pick any whole number from 1 to 10,000.

\sqrt{412} = 2\sqrt{103} \approx 20.297783

How to work it out

1
The square root of 412 is the number that multiplied by itself gives 412.
2
412 is between the perfect squares 20² = 400 and 21² = 441, so its square root is between 20 and 21.
3
Pull out the biggest square factor: 412 = 4 × 103, so
$\sqrt{412} = \sqrt{4 \times 103} = 2\sqrt{103}$
4
A calculator, or long division of digits, gives
$\sqrt{412} \approx 20.297783$

LaTeX source of the formulas on this page

\[ \sqrt{412} = 2\sqrt{103} \approx 20.297783 \]
\[ \sqrt{412} = \sqrt{4 \times 103} = 2\sqrt{103} \]
\[ \sqrt{412} \approx 20.297783 \]

What is the square root of 412?

The square root of 412 is 20.297783 (rounded to 6 decimal places). In simplest radical form it is 2√103.

Is 412 a perfect square?

No. It lies between 20² = 400 and 21² = 441.

What is 412 squared?

412 × 412 = 169744.

What is the square root of 412 rounded to 2 decimals?

20.30.