Square root of 6756

The square root of 6756 is 82.19489 (rounded to 6 decimal places). In simplest radical form it is 2√1689.

Square root of 6756

Pick any whole number from 1 to 10,000.

\sqrt{6756} = 2\sqrt{1689} \approx 82.19489

How to work it out

1
The square root of 6756 is the number that multiplied by itself gives 6756.
2
6756 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: 6756 = 4 × 1689, so
$\sqrt{6756} = \sqrt{4 \times 1689} = 2\sqrt{1689}$
4
A calculator, or long division of digits, gives
$\sqrt{6756} \approx 82.19489$

LaTeX source of the formulas on this page

\[ \sqrt{6756} = 2\sqrt{1689} \approx 82.19489 \]
\[ \sqrt{6756} = \sqrt{4 \times 1689} = 2\sqrt{1689} \]
\[ \sqrt{6756} \approx 82.19489 \]

What is the square root of 6756?

The square root of 6756 is 82.19489 (rounded to 6 decimal places). In simplest radical form it is 2√1689.

Is 6756 a perfect square?

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

What is 6756 squared?

6756 × 6756 = 45643536.

What is the square root of 6756 rounded to 2 decimals?

82.19.