Square root of 384

The square root of 384 is 19.595918 (rounded to 6 decimal places). In simplest radical form it is 8√6.

Square root of 384

Pick any whole number from 1 to 10,000.

\sqrt{384} = 8\sqrt{6} \approx 19.595918

How to work it out

1
The square root of 384 is the number that multiplied by itself gives 384.
2
384 is between the perfect squares 19² = 361 and 20² = 400, so its square root is between 19 and 20.
3
Pull out the biggest square factor: 384 = 64 × 6, so
$\sqrt{384} = \sqrt{64 \times 6} = 8\sqrt{6}$
4
A calculator, or long division of digits, gives
$\sqrt{384} \approx 19.595918$

LaTeX source of the formulas on this page

\[ \sqrt{384} = 8\sqrt{6} \approx 19.595918 \]
\[ \sqrt{384} = \sqrt{64 \times 6} = 8\sqrt{6} \]
\[ \sqrt{384} \approx 19.595918 \]

What is the square root of 384?

The square root of 384 is 19.595918 (rounded to 6 decimal places). In simplest radical form it is 8√6.

Is 384 a perfect square?

No. It lies between 19² = 361 and 20² = 400.

What is 384 squared?

384 × 384 = 147456.

What is the square root of 384 rounded to 2 decimals?

19.60.