Square root of 6824

The square root of 6824 is 82.607506 (rounded to 6 decimal places). In simplest radical form it is 2√1706.

Square root of 6824

Pick any whole number from 1 to 10,000.

\sqrt{6824} = 2\sqrt{1706} \approx 82.607506

How to work it out

1
The square root of 6824 is the number that multiplied by itself gives 6824.
2
6824 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: 6824 = 4 × 1706, so
$\sqrt{6824} = \sqrt{4 \times 1706} = 2\sqrt{1706}$
4
A calculator, or long division of digits, gives
$\sqrt{6824} \approx 82.607506$

LaTeX source of the formulas on this page

\[ \sqrt{6824} = 2\sqrt{1706} \approx 82.607506 \]
\[ \sqrt{6824} = \sqrt{4 \times 1706} = 2\sqrt{1706} \]
\[ \sqrt{6824} \approx 82.607506 \]

What is the square root of 6824?

The square root of 6824 is 82.607506 (rounded to 6 decimal places). In simplest radical form it is 2√1706.

Is 6824 a perfect square?

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

What is 6824 squared?

6824 × 6824 = 46566976.

What is the square root of 6824 rounded to 2 decimals?

82.61.