Square root of 3006

The square root of 3006 is 54.827001 (rounded to 6 decimal places). In simplest radical form it is 3√334.

Square root of 3006

Pick any whole number from 1 to 10,000.

\sqrt{3006} = 3\sqrt{334} \approx 54.827001

How to work it out

1
The square root of 3006 is the number that multiplied by itself gives 3006.
2
3006 is between the perfect squares 54² = 2916 and 55² = 3025, so its square root is between 54 and 55.
3
Pull out the biggest square factor: 3006 = 9 × 334, so
$\sqrt{3006} = \sqrt{9 \times 334} = 3\sqrt{334}$
4
A calculator, or long division of digits, gives
$\sqrt{3006} \approx 54.827001$

LaTeX source of the formulas on this page

\[ \sqrt{3006} = 3\sqrt{334} \approx 54.827001 \]
\[ \sqrt{3006} = \sqrt{9 \times 334} = 3\sqrt{334} \]
\[ \sqrt{3006} \approx 54.827001 \]

What is the square root of 3006?

The square root of 3006 is 54.827001 (rounded to 6 decimal places). In simplest radical form it is 3√334.

Is 3006 a perfect square?

No. It lies between 54² = 2916 and 55² = 3025.

What is 3006 squared?

3006 × 3006 = 9036036.

What is the square root of 3006 rounded to 2 decimals?

54.83.