Square root of 500

The square root of 500 is 22.36068 (rounded to 6 decimal places). In simplest radical form it is 10√5.

Square root of 500

Pick any whole number from 1 to 10,000.

\sqrt{500} = 10\sqrt{5} \approx 22.36068

How to work it out

1
The square root of 500 is the number that multiplied by itself gives 500.
2
500 is between the perfect squares 22² = 484 and 23² = 529, so its square root is between 22 and 23.
3
Pull out the biggest square factor: 500 = 100 × 5, so
$\sqrt{500} = \sqrt{100 \times 5} = 10\sqrt{5}$
4
A calculator, or long division of digits, gives
$\sqrt{500} \approx 22.36068$

LaTeX source of the formulas on this page

\[ \sqrt{500} = 10\sqrt{5} \approx 22.36068 \]
\[ \sqrt{500} = \sqrt{100 \times 5} = 10\sqrt{5} \]
\[ \sqrt{500} \approx 22.36068 \]

What is the square root of 500?

The square root of 500 is 22.36068 (rounded to 6 decimal places). In simplest radical form it is 10√5.

Is 500 a perfect square?

No. It lies between 22² = 484 and 23² = 529.

What is 500 squared?

500 × 500 = 250000.

What is the square root of 500 rounded to 2 decimals?

22.36.