Square root of 2166

The square root of 2166 is 46.540305 (rounded to 6 decimal places). In simplest radical form it is 19√6.

Square root of 2166

Pick any whole number from 1 to 10,000.

\sqrt{2166} = 19\sqrt{6} \approx 46.540305

How to work it out

1
The square root of 2166 is the number that multiplied by itself gives 2166.
2
2166 is between the perfect squares 46² = 2116 and 47² = 2209, so its square root is between 46 and 47.
3
Pull out the biggest square factor: 2166 = 361 × 6, so
$\sqrt{2166} = \sqrt{361 \times 6} = 19\sqrt{6}$
4
A calculator, or long division of digits, gives
$\sqrt{2166} \approx 46.540305$

LaTeX source of the formulas on this page

\[ \sqrt{2166} = 19\sqrt{6} \approx 46.540305 \]
\[ \sqrt{2166} = \sqrt{361 \times 6} = 19\sqrt{6} \]
\[ \sqrt{2166} \approx 46.540305 \]

What is the square root of 2166?

The square root of 2166 is 46.540305 (rounded to 6 decimal places). In simplest radical form it is 19√6.

Is 2166 a perfect square?

No. It lies between 46² = 2116 and 47² = 2209.

What is 2166 squared?

2166 × 2166 = 4691556.

What is the square root of 2166 rounded to 2 decimals?

46.54.