Square root of 8164

The square root of 8164 is 90.354856 (rounded to 6 decimal places). In simplest radical form it is 2√2041.

Square root of 8164

Pick any whole number from 1 to 10,000.

\sqrt{8164} = 2\sqrt{2041} \approx 90.354856

How to work it out

1
The square root of 8164 is the number that multiplied by itself gives 8164.
2
8164 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: 8164 = 4 × 2041, so
$\sqrt{8164} = \sqrt{4 \times 2041} = 2\sqrt{2041}$
4
A calculator, or long division of digits, gives
$\sqrt{8164} \approx 90.354856$

LaTeX source of the formulas on this page

\[ \sqrt{8164} = 2\sqrt{2041} \approx 90.354856 \]
\[ \sqrt{8164} = \sqrt{4 \times 2041} = 2\sqrt{2041} \]
\[ \sqrt{8164} \approx 90.354856 \]

What is the square root of 8164?

The square root of 8164 is 90.354856 (rounded to 6 decimal places). In simplest radical form it is 2√2041.

Is 8164 a perfect square?

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

What is 8164 squared?

8164 × 8164 = 66650896.

What is the square root of 8164 rounded to 2 decimals?

90.35.