Square root of 392

The square root of 392 is 19.79899 (rounded to 6 decimal places). In simplest radical form it is 14√2.

Square root of 392

Pick any whole number from 1 to 10,000.

\sqrt{392} = 14\sqrt{2} \approx 19.79899

How to work it out

1
The square root of 392 is the number that multiplied by itself gives 392.
2
392 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: 392 = 196 × 2, so
$\sqrt{392} = \sqrt{196 \times 2} = 14\sqrt{2}$
4
A calculator, or long division of digits, gives
$\sqrt{392} \approx 19.79899$

LaTeX source of the formulas on this page

\[ \sqrt{392} = 14\sqrt{2} \approx 19.79899 \]
\[ \sqrt{392} = \sqrt{196 \times 2} = 14\sqrt{2} \]
\[ \sqrt{392} \approx 19.79899 \]

What is the square root of 392?

The square root of 392 is 19.79899 (rounded to 6 decimal places). In simplest radical form it is 14√2.

Is 392 a perfect square?

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

What is 392 squared?

392 × 392 = 153664.

What is the square root of 392 rounded to 2 decimals?

19.80.