Square root of 2197

The square root of 2197 is 46.872167 (rounded to 6 decimal places). In simplest radical form it is 13√13.

Square root of 2197

Pick any whole number from 1 to 10,000.

\sqrt{2197} = 13\sqrt{13} \approx 46.872167

How to work it out

1
The square root of 2197 is the number that multiplied by itself gives 2197.
2
2197 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: 2197 = 169 × 13, so
$\sqrt{2197} = \sqrt{169 \times 13} = 13\sqrt{13}$
4
A calculator, or long division of digits, gives
$\sqrt{2197} \approx 46.872167$

LaTeX source of the formulas on this page

\[ \sqrt{2197} = 13\sqrt{13} \approx 46.872167 \]
\[ \sqrt{2197} = \sqrt{169 \times 13} = 13\sqrt{13} \]
\[ \sqrt{2197} \approx 46.872167 \]

What is the square root of 2197?

The square root of 2197 is 46.872167 (rounded to 6 decimal places). In simplest radical form it is 13√13.

Is 2197 a perfect square?

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

What is 2197 squared?

2197 × 2197 = 4826809.

What is the square root of 2197 rounded to 2 decimals?

46.87.