Square root of 6864

The square root of 6864 is 82.849261 (rounded to 6 decimal places). In simplest radical form it is 4√429.

Square root of 6864

Pick any whole number from 1 to 10,000.

\sqrt{6864} = 4\sqrt{429} \approx 82.849261

How to work it out

1
The square root of 6864 is the number that multiplied by itself gives 6864.
2
6864 is between the perfect squares 82² = 6724 and 83² = 6889, so its square root is between 82 and 83.
3
Pull out the biggest square factor: 6864 = 16 × 429, so
$\sqrt{6864} = \sqrt{16 \times 429} = 4\sqrt{429}$
4
A calculator, or long division of digits, gives
$\sqrt{6864} \approx 82.849261$

LaTeX source of the formulas on this page

\[ \sqrt{6864} = 4\sqrt{429} \approx 82.849261 \]
\[ \sqrt{6864} = \sqrt{16 \times 429} = 4\sqrt{429} \]
\[ \sqrt{6864} \approx 82.849261 \]

What is the square root of 6864?

The square root of 6864 is 82.849261 (rounded to 6 decimal places). In simplest radical form it is 4√429.

Is 6864 a perfect square?

No. It lies between 82² = 6724 and 83² = 6889.

What is 6864 squared?

6864 × 6864 = 47114496.

What is the square root of 6864 rounded to 2 decimals?

82.85.