Square root of 2254

The square root of 2254 is 47.47631 (rounded to 6 decimal places). In simplest radical form it is 7√46.

Square root of 2254

Pick any whole number from 1 to 10,000.

\sqrt{2254} = 7\sqrt{46} \approx 47.47631

How to work it out

1
The square root of 2254 is the number that multiplied by itself gives 2254.
2
2254 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: 2254 = 49 × 46, so
$\sqrt{2254} = \sqrt{49 \times 46} = 7\sqrt{46}$
4
A calculator, or long division of digits, gives
$\sqrt{2254} \approx 47.47631$

LaTeX source of the formulas on this page

\[ \sqrt{2254} = 7\sqrt{46} \approx 47.47631 \]
\[ \sqrt{2254} = \sqrt{49 \times 46} = 7\sqrt{46} \]
\[ \sqrt{2254} \approx 47.47631 \]

What is the square root of 2254?

The square root of 2254 is 47.47631 (rounded to 6 decimal places). In simplest radical form it is 7√46.

Is 2254 a perfect square?

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

What is 2254 squared?

2254 × 2254 = 5080516.

What is the square root of 2254 rounded to 2 decimals?

47.48.