Square root of 507

The square root of 507 is 22.51666 (rounded to 6 decimal places). In simplest radical form it is 13√3.

Square root of 507

Pick any whole number from 1 to 10,000.

\sqrt{507} = 13\sqrt{3} \approx 22.51666

How to work it out

1
The square root of 507 is the number that multiplied by itself gives 507.
2
507 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: 507 = 169 × 3, so
$\sqrt{507} = \sqrt{169 \times 3} = 13\sqrt{3}$
4
A calculator, or long division of digits, gives
$\sqrt{507} \approx 22.51666$

LaTeX source of the formulas on this page

\[ \sqrt{507} = 13\sqrt{3} \approx 22.51666 \]
\[ \sqrt{507} = \sqrt{169 \times 3} = 13\sqrt{3} \]
\[ \sqrt{507} \approx 22.51666 \]

What is the square root of 507?

The square root of 507 is 22.51666 (rounded to 6 decimal places). In simplest radical form it is 13√3.

Is 507 a perfect square?

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

What is 507 squared?

507 × 507 = 257049.

What is the square root of 507 rounded to 2 decimals?

22.52.