Square root of 513

The square root of 513 is 22.649503 (rounded to 6 decimal places). In simplest radical form it is 3√57.

Square root of 513

Pick any whole number from 1 to 10,000.

\sqrt{513} = 3\sqrt{57} \approx 22.649503

How to work it out

1
The square root of 513 is the number that multiplied by itself gives 513.
2
513 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: 513 = 9 × 57, so
$\sqrt{513} = \sqrt{9 \times 57} = 3\sqrt{57}$
4
A calculator, or long division of digits, gives
$\sqrt{513} \approx 22.649503$

LaTeX source of the formulas on this page

\[ \sqrt{513} = 3\sqrt{57} \approx 22.649503 \]
\[ \sqrt{513} = \sqrt{9 \times 57} = 3\sqrt{57} \]
\[ \sqrt{513} \approx 22.649503 \]

What is the square root of 513?

The square root of 513 is 22.649503 (rounded to 6 decimal places). In simplest radical form it is 3√57.

Is 513 a perfect square?

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

What is 513 squared?

513 × 513 = 263169.

What is the square root of 513 rounded to 2 decimals?

22.65.