Square root of 6784

The square root of 6784 is 82.365041 (rounded to 6 decimal places). In simplest radical form it is 8√106.

Square root of 6784

Pick any whole number from 1 to 10,000.

\sqrt{6784} = 8\sqrt{106} \approx 82.365041

How to work it out

1
The square root of 6784 is the number that multiplied by itself gives 6784.
2
6784 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: 6784 = 64 × 106, so
$\sqrt{6784} = \sqrt{64 \times 106} = 8\sqrt{106}$
4
A calculator, or long division of digits, gives
$\sqrt{6784} \approx 82.365041$

LaTeX source of the formulas on this page

\[ \sqrt{6784} = 8\sqrt{106} \approx 82.365041 \]
\[ \sqrt{6784} = \sqrt{64 \times 106} = 8\sqrt{106} \]
\[ \sqrt{6784} \approx 82.365041 \]

What is the square root of 6784?

The square root of 6784 is 82.365041 (rounded to 6 decimal places). In simplest radical form it is 8√106.

Is 6784 a perfect square?

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

What is 6784 squared?

6784 × 6784 = 46022656.

What is the square root of 6784 rounded to 2 decimals?

82.37.