Square root of 4000

The square root of 4000 is 63.245553 (rounded to 6 decimal places). In simplest radical form it is 20√10.

Square root of 4000

Pick any whole number from 1 to 10,000.

\sqrt{4000} = 20\sqrt{10} \approx 63.245553

How to work it out

1
The square root of 4000 is the number that multiplied by itself gives 4000.
2
4000 is between the perfect squares 63² = 3969 and 64² = 4096, so its square root is between 63 and 64.
3
Pull out the biggest square factor: 4000 = 400 × 10, so
$\sqrt{4000} = \sqrt{400 \times 10} = 20\sqrt{10}$
4
A calculator, or long division of digits, gives
$\sqrt{4000} \approx 63.245553$

LaTeX source of the formulas on this page

\[ \sqrt{4000} = 20\sqrt{10} \approx 63.245553 \]
\[ \sqrt{4000} = \sqrt{400 \times 10} = 20\sqrt{10} \]
\[ \sqrt{4000} \approx 63.245553 \]

What is the square root of 4000?

The square root of 4000 is 63.245553 (rounded to 6 decimal places). In simplest radical form it is 20√10.

Is 4000 a perfect square?

No. It lies between 63² = 3969 and 64² = 4096.

What is 4000 squared?

4000 × 4000 = 16000000.

What is the square root of 4000 rounded to 2 decimals?

63.25.