Square root of 2048

The square root of 2048 is 45.254834 (rounded to 6 decimal places). In simplest radical form it is 32√2.

Square root of 2048

Pick any whole number from 1 to 10,000.

\sqrt{2048} = 32\sqrt{2} \approx 45.254834

How to work it out

1
The square root of 2048 is the number that multiplied by itself gives 2048.
2
2048 is between the perfect squares 45² = 2025 and 46² = 2116, so its square root is between 45 and 46.
3
Pull out the biggest square factor: 2048 = 1024 × 2, so
$\sqrt{2048} = \sqrt{1024 \times 2} = 32\sqrt{2}$
4
A calculator, or long division of digits, gives
$\sqrt{2048} \approx 45.254834$

LaTeX source of the formulas on this page

\[ \sqrt{2048} = 32\sqrt{2} \approx 45.254834 \]
\[ \sqrt{2048} = \sqrt{1024 \times 2} = 32\sqrt{2} \]
\[ \sqrt{2048} \approx 45.254834 \]

What is the square root of 2048?

The square root of 2048 is 45.254834 (rounded to 6 decimal places). In simplest radical form it is 32√2.

Is 2048 a perfect square?

No. It lies between 45² = 2025 and 46² = 2116.

What is 2048 squared?

2048 × 2048 = 4194304.

What is the square root of 2048 rounded to 2 decimals?

45.25.