Square root of 8214

The square root of 8214 is 90.63112 (rounded to 6 decimal places). In simplest radical form it is 37√6.

Square root of 8214

Pick any whole number from 1 to 10,000.

\sqrt{8214} = 37\sqrt{6} \approx 90.63112

How to work it out

1
The square root of 8214 is the number that multiplied by itself gives 8214.
2
8214 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: 8214 = 1369 × 6, so
$\sqrt{8214} = \sqrt{1369 \times 6} = 37\sqrt{6}$
4
A calculator, or long division of digits, gives
$\sqrt{8214} \approx 90.63112$

LaTeX source of the formulas on this page

\[ \sqrt{8214} = 37\sqrt{6} \approx 90.63112 \]
\[ \sqrt{8214} = \sqrt{1369 \times 6} = 37\sqrt{6} \]
\[ \sqrt{8214} \approx 90.63112 \]

What is the square root of 8214?

The square root of 8214 is 90.63112 (rounded to 6 decimal places). In simplest radical form it is 37√6.

Is 8214 a perfect square?

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

What is 8214 squared?

8214 × 8214 = 67469796.

What is the square root of 8214 rounded to 2 decimals?

90.63.