Square root of 6000

The square root of 6000 is 77.459667 (rounded to 6 decimal places). In simplest radical form it is 20√15.

Square root of 6000

Pick any whole number from 1 to 10,000.

\sqrt{6000} = 20\sqrt{15} \approx 77.459667

How to work it out

1
The square root of 6000 is the number that multiplied by itself gives 6000.
2
6000 is between the perfect squares 77² = 5929 and 78² = 6084, so its square root is between 77 and 78.
3
Pull out the biggest square factor: 6000 = 400 × 15, so
$\sqrt{6000} = \sqrt{400 \times 15} = 20\sqrt{15}$
4
A calculator, or long division of digits, gives
$\sqrt{6000} \approx 77.459667$

LaTeX source of the formulas on this page

\[ \sqrt{6000} = 20\sqrt{15} \approx 77.459667 \]
\[ \sqrt{6000} = \sqrt{400 \times 15} = 20\sqrt{15} \]
\[ \sqrt{6000} \approx 77.459667 \]

What is the square root of 6000?

The square root of 6000 is 77.459667 (rounded to 6 decimal places). In simplest radical form it is 20√15.

Is 6000 a perfect square?

No. It lies between 77² = 5929 and 78² = 6084.

What is 6000 squared?

6000 × 6000 = 36000000.

What is the square root of 6000 rounded to 2 decimals?

77.46.