Square root of 524

The square root of 524 is 22.891046 (rounded to 6 decimal places). In simplest radical form it is 2√131.

Square root of 524

Pick any whole number from 1 to 10,000.

\sqrt{524} = 2\sqrt{131} \approx 22.891046

How to work it out

1
The square root of 524 is the number that multiplied by itself gives 524.
2
524 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: 524 = 4 × 131, so
$\sqrt{524} = \sqrt{4 \times 131} = 2\sqrt{131}$
4
A calculator, or long division of digits, gives
$\sqrt{524} \approx 22.891046$

LaTeX source of the formulas on this page

\[ \sqrt{524} = 2\sqrt{131} \approx 22.891046 \]
\[ \sqrt{524} = \sqrt{4 \times 131} = 2\sqrt{131} \]
\[ \sqrt{524} \approx 22.891046 \]

What is the square root of 524?

The square root of 524 is 22.891046 (rounded to 6 decimal places). In simplest radical form it is 2√131.

Is 524 a perfect square?

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

What is 524 squared?

524 × 524 = 274576.

What is the square root of 524 rounded to 2 decimals?

22.89.