Square root of 768

The square root of 768 is 27.712813 (rounded to 6 decimal places). In simplest radical form it is 16√3.

Square root of 768

Pick any whole number from 1 to 10,000.

\sqrt{768} = 16\sqrt{3} \approx 27.712813

How to work it out

1
The square root of 768 is the number that multiplied by itself gives 768.
2
768 is between the perfect squares 27² = 729 and 28² = 784, so its square root is between 27 and 28.
3
Pull out the biggest square factor: 768 = 256 × 3, so
$\sqrt{768} = \sqrt{256 \times 3} = 16\sqrt{3}$
4
A calculator, or long division of digits, gives
$\sqrt{768} \approx 27.712813$

LaTeX source of the formulas on this page

\[ \sqrt{768} = 16\sqrt{3} \approx 27.712813 \]
\[ \sqrt{768} = \sqrt{256 \times 3} = 16\sqrt{3} \]
\[ \sqrt{768} \approx 27.712813 \]

What is the square root of 768?

The square root of 768 is 27.712813 (rounded to 6 decimal places). In simplest radical form it is 16√3.

Is 768 a perfect square?

No. It lies between 27² = 729 and 28² = 784.

What is 768 squared?

768 × 768 = 589824.

What is the square root of 768 rounded to 2 decimals?

27.71.