Square root of 2252

The square root of 2252 is 47.455242 (rounded to 6 decimal places). In simplest radical form it is 2√563.

Square root of 2252

Pick any whole number from 1 to 10,000.

\sqrt{2252} = 2\sqrt{563} \approx 47.455242

How to work it out

1
The square root of 2252 is the number that multiplied by itself gives 2252.
2
2252 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: 2252 = 4 × 563, so
$\sqrt{2252} = \sqrt{4 \times 563} = 2\sqrt{563}$
4
A calculator, or long division of digits, gives
$\sqrt{2252} \approx 47.455242$

LaTeX source of the formulas on this page

\[ \sqrt{2252} = 2\sqrt{563} \approx 47.455242 \]
\[ \sqrt{2252} = \sqrt{4 \times 563} = 2\sqrt{563} \]
\[ \sqrt{2252} \approx 47.455242 \]

What is the square root of 2252?

The square root of 2252 is 47.455242 (rounded to 6 decimal places). In simplest radical form it is 2√563.

Is 2252 a perfect square?

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

What is 2252 squared?

2252 × 2252 = 5071504.

What is the square root of 2252 rounded to 2 decimals?

47.46.