Square root of 512

The square root of 512 is 22.627417 (rounded to 6 decimal places). In simplest radical form it is 16√2.

Square root of 512

Pick any whole number from 1 to 10,000.

\sqrt{512} = 16\sqrt{2} \approx 22.627417

How to work it out

1
The square root of 512 is the number that multiplied by itself gives 512.
2
512 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: 512 = 256 × 2, so
$\sqrt{512} = \sqrt{256 \times 2} = 16\sqrt{2}$
4
A calculator, or long division of digits, gives
$\sqrt{512} \approx 22.627417$

LaTeX source of the formulas on this page

\[ \sqrt{512} = 16\sqrt{2} \approx 22.627417 \]
\[ \sqrt{512} = \sqrt{256 \times 2} = 16\sqrt{2} \]
\[ \sqrt{512} \approx 22.627417 \]

What is the square root of 512?

The square root of 512 is 22.627417 (rounded to 6 decimal places). In simplest radical form it is 16√2.

Is 512 a perfect square?

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

What is 512 squared?

512 × 512 = 262144.

What is the square root of 512 rounded to 2 decimals?

22.63.