Square root of 5664

The square root of 5664 is 75.259551 (rounded to 6 decimal places). In simplest radical form it is 4√354.

Square root of 5664

Pick any whole number from 1 to 10,000.

\sqrt{5664} = 4\sqrt{354} \approx 75.259551

How to work it out

1
The square root of 5664 is the number that multiplied by itself gives 5664.
2
5664 is between the perfect squares 75² = 5625 and 76² = 5776, so its square root is between 75 and 76.
3
Pull out the biggest square factor: 5664 = 16 × 354, so
$\sqrt{5664} = \sqrt{16 \times 354} = 4\sqrt{354}$
4
A calculator, or long division of digits, gives
$\sqrt{5664} \approx 75.259551$

LaTeX source of the formulas on this page

\[ \sqrt{5664} = 4\sqrt{354} \approx 75.259551 \]
\[ \sqrt{5664} = \sqrt{16 \times 354} = 4\sqrt{354} \]
\[ \sqrt{5664} \approx 75.259551 \]

What is the square root of 5664?

The square root of 5664 is 75.259551 (rounded to 6 decimal places). In simplest radical form it is 4√354.

Is 5664 a perfect square?

No. It lies between 75² = 5625 and 76² = 5776.

What is 5664 squared?

5664 × 5664 = 32080896.

What is the square root of 5664 rounded to 2 decimals?

75.26.