Square root of 999

The square root of 999 is 31.606961 (rounded to 6 decimal places). In simplest radical form it is 3√111.

Square root of 999

Pick any whole number from 1 to 10,000.

\sqrt{999} = 3\sqrt{111} \approx 31.606961

How to work it out

1
The square root of 999 is the number that multiplied by itself gives 999.
2
999 is between the perfect squares 31² = 961 and 32² = 1024, so its square root is between 31 and 32.
3
Pull out the biggest square factor: 999 = 9 × 111, so
$\sqrt{999} = \sqrt{9 \times 111} = 3\sqrt{111}$
4
A calculator, or long division of digits, gives
$\sqrt{999} \approx 31.606961$

LaTeX source of the formulas on this page

\[ \sqrt{999} = 3\sqrt{111} \approx 31.606961 \]
\[ \sqrt{999} = \sqrt{9 \times 111} = 3\sqrt{111} \]
\[ \sqrt{999} \approx 31.606961 \]

What is the square root of 999?

The square root of 999 is 31.606961 (rounded to 6 decimal places). In simplest radical form it is 3√111.

Is 999 a perfect square?

No. It lies between 31² = 961 and 32² = 1024.

What is 999 squared?

999 × 999 = 998001.

What is the square root of 999 rounded to 2 decimals?

31.61.