Square root of 8224

The square root of 8224 is 90.686272 (rounded to 6 decimal places). In simplest radical form it is 4√514.

Square root of 8224

Pick any whole number from 1 to 10,000.

\sqrt{8224} = 4\sqrt{514} \approx 90.686272

How to work it out

1
The square root of 8224 is the number that multiplied by itself gives 8224.
2
8224 is between the perfect squares 90² = 8100 and 91² = 8281, so its square root is between 90 and 91.
3
Pull out the biggest square factor: 8224 = 16 × 514, so
$\sqrt{8224} = \sqrt{16 \times 514} = 4\sqrt{514}$
4
A calculator, or long division of digits, gives
$\sqrt{8224} \approx 90.686272$

LaTeX source of the formulas on this page

\[ \sqrt{8224} = 4\sqrt{514} \approx 90.686272 \]
\[ \sqrt{8224} = \sqrt{16 \times 514} = 4\sqrt{514} \]
\[ \sqrt{8224} \approx 90.686272 \]

What is the square root of 8224?

The square root of 8224 is 90.686272 (rounded to 6 decimal places). In simplest radical form it is 4√514.

Is 8224 a perfect square?

No. It lies between 90² = 8100 and 91² = 8281.

What is 8224 squared?

8224 × 8224 = 67634176.

What is the square root of 8224 rounded to 2 decimals?

90.69.