Square root of 4564

The square root of 4564 is 67.557383 (rounded to 6 decimal places). In simplest radical form it is 2√1141.

Square root of 4564

Pick any whole number from 1 to 10,000.

\sqrt{4564} = 2\sqrt{1141} \approx 67.557383

How to work it out

1
The square root of 4564 is the number that multiplied by itself gives 4564.
2
4564 is between the perfect squares 67² = 4489 and 68² = 4624, so its square root is between 67 and 68.
3
Pull out the biggest square factor: 4564 = 4 × 1141, so
$\sqrt{4564} = \sqrt{4 \times 1141} = 2\sqrt{1141}$
4
A calculator, or long division of digits, gives
$\sqrt{4564} \approx 67.557383$

LaTeX source of the formulas on this page

\[ \sqrt{4564} = 2\sqrt{1141} \approx 67.557383 \]
\[ \sqrt{4564} = \sqrt{4 \times 1141} = 2\sqrt{1141} \]
\[ \sqrt{4564} \approx 67.557383 \]

What is the square root of 4564?

The square root of 4564 is 67.557383 (rounded to 6 decimal places). In simplest radical form it is 2√1141.

Is 4564 a perfect square?

No. It lies between 67² = 4489 and 68² = 4624.

What is 4564 squared?

4564 × 4564 = 20830096.

What is the square root of 4564 rounded to 2 decimals?

67.56.