Square root of 2272

The square root of 2272 is 47.665501 (rounded to 6 decimal places). In simplest radical form it is 4√142.

Square root of 2272

Pick any whole number from 1 to 10,000.

\sqrt{2272} = 4\sqrt{142} \approx 47.665501

How to work it out

1
The square root of 2272 is the number that multiplied by itself gives 2272.
2
2272 is between the perfect squares 47² = 2209 and 48² = 2304, so its square root is between 47 and 48.
3
Pull out the biggest square factor: 2272 = 16 × 142, so
$\sqrt{2272} = \sqrt{16 \times 142} = 4\sqrt{142}$
4
A calculator, or long division of digits, gives
$\sqrt{2272} \approx 47.665501$

LaTeX source of the formulas on this page

\[ \sqrt{2272} = 4\sqrt{142} \approx 47.665501 \]
\[ \sqrt{2272} = \sqrt{16 \times 142} = 4\sqrt{142} \]
\[ \sqrt{2272} \approx 47.665501 \]

What is the square root of 2272?

The square root of 2272 is 47.665501 (rounded to 6 decimal places). In simplest radical form it is 4√142.

Is 2272 a perfect square?

No. It lies between 47² = 2209 and 48² = 2304.

What is 2272 squared?

2272 × 2272 = 5161984.

What is the square root of 2272 rounded to 2 decimals?

47.67.