Square root of 2084

The square root of 2084 is 45.650849 (rounded to 6 decimal places). In simplest radical form it is 2√521.

Square root of 2084

Pick any whole number from 1 to 10,000.

\sqrt{2084} = 2\sqrt{521} \approx 45.650849

How to work it out

1
The square root of 2084 is the number that multiplied by itself gives 2084.
2
2084 is between the perfect squares 45² = 2025 and 46² = 2116, so its square root is between 45 and 46.
3
Pull out the biggest square factor: 2084 = 4 × 521, so
$\sqrt{2084} = \sqrt{4 \times 521} = 2\sqrt{521}$
4
A calculator, or long division of digits, gives
$\sqrt{2084} \approx 45.650849$

LaTeX source of the formulas on this page

\[ \sqrt{2084} = 2\sqrt{521} \approx 45.650849 \]
\[ \sqrt{2084} = \sqrt{4 \times 521} = 2\sqrt{521} \]
\[ \sqrt{2084} \approx 45.650849 \]

What is the square root of 2084?

The square root of 2084 is 45.650849 (rounded to 6 decimal places). In simplest radical form it is 2√521.

Is 2084 a perfect square?

No. It lies between 45² = 2025 and 46² = 2116.

What is 2084 squared?

2084 × 2084 = 4343056.

What is the square root of 2084 rounded to 2 decimals?

45.65.