Square root of 8564

The square root of 8564 is 92.541882 (rounded to 6 decimal places). In simplest radical form it is 2√2141.

Square root of 8564

Pick any whole number from 1 to 10,000.

\sqrt{8564} = 2\sqrt{2141} \approx 92.541882

How to work it out

1
The square root of 8564 is the number that multiplied by itself gives 8564.
2
8564 is between the perfect squares 92² = 8464 and 93² = 8649, so its square root is between 92 and 93.
3
Pull out the biggest square factor: 8564 = 4 × 2141, so
$\sqrt{8564} = \sqrt{4 \times 2141} = 2\sqrt{2141}$
4
A calculator, or long division of digits, gives
$\sqrt{8564} \approx 92.541882$

LaTeX source of the formulas on this page

\[ \sqrt{8564} = 2\sqrt{2141} \approx 92.541882 \]
\[ \sqrt{8564} = \sqrt{4 \times 2141} = 2\sqrt{2141} \]
\[ \sqrt{8564} \approx 92.541882 \]

What is the square root of 8564?

The square root of 8564 is 92.541882 (rounded to 6 decimal places). In simplest radical form it is 2√2141.

Is 8564 a perfect square?

No. It lies between 92² = 8464 and 93² = 8649.

What is 8564 squared?

8564 × 8564 = 73342096.

What is the square root of 8564 rounded to 2 decimals?

92.54.