Square root of 1680

The square root of 1680 is 40.987803 (rounded to 6 decimal places). In simplest radical form it is 4√105.

Square root of 1680

Pick any whole number from 1 to 10,000.

\sqrt{1680} = 4\sqrt{105} \approx 40.987803

How to work it out

1
The square root of 1680 is the number that multiplied by itself gives 1680.
2
1680 is between the perfect squares 40² = 1600 and 41² = 1681, so its square root is between 40 and 41.
3
Pull out the biggest square factor: 1680 = 16 × 105, so
$\sqrt{1680} = \sqrt{16 \times 105} = 4\sqrt{105}$
4
A calculator, or long division of digits, gives
$\sqrt{1680} \approx 40.987803$

LaTeX source of the formulas on this page

\[ \sqrt{1680} = 4\sqrt{105} \approx 40.987803 \]
\[ \sqrt{1680} = \sqrt{16 \times 105} = 4\sqrt{105} \]
\[ \sqrt{1680} \approx 40.987803 \]

What is the square root of 1680?

The square root of 1680 is 40.987803 (rounded to 6 decimal places). In simplest radical form it is 4√105.

Is 1680 a perfect square?

No. It lies between 40² = 1600 and 41² = 1681.

What is 1680 squared?

1680 × 1680 = 2822400.

What is the square root of 1680 rounded to 2 decimals?

40.99.