Square root of 2004

The square root of 2004 is 44.766059 (rounded to 6 decimal places). In simplest radical form it is 2√501.

Square root of 2004

Pick any whole number from 1 to 10,000.

\sqrt{2004} = 2\sqrt{501} \approx 44.766059

How to work it out

1
The square root of 2004 is the number that multiplied by itself gives 2004.
2
2004 is between the perfect squares 44² = 1936 and 45² = 2025, so its square root is between 44 and 45.
3
Pull out the biggest square factor: 2004 = 4 × 501, so
$\sqrt{2004} = \sqrt{4 \times 501} = 2\sqrt{501}$
4
A calculator, or long division of digits, gives
$\sqrt{2004} \approx 44.766059$

LaTeX source of the formulas on this page

\[ \sqrt{2004} = 2\sqrt{501} \approx 44.766059 \]
\[ \sqrt{2004} = \sqrt{4 \times 501} = 2\sqrt{501} \]
\[ \sqrt{2004} \approx 44.766059 \]

What is the square root of 2004?

The square root of 2004 is 44.766059 (rounded to 6 decimal places). In simplest radical form it is 2√501.

Is 2004 a perfect square?

No. It lies between 44² = 1936 and 45² = 2025.

What is 2004 squared?

2004 × 2004 = 4016016.

What is the square root of 2004 rounded to 2 decimals?

44.77.