Square root of 338

The square root of 338 is 18.384776 (rounded to 6 decimal places). In simplest radical form it is 13√2.

Square root of 338

Pick any whole number from 1 to 10,000.

\sqrt{338} = 13\sqrt{2} \approx 18.384776

How to work it out

1
The square root of 338 is the number that multiplied by itself gives 338.
2
338 is between the perfect squares 18² = 324 and 19² = 361, so its square root is between 18 and 19.
3
Pull out the biggest square factor: 338 = 169 × 2, so
$\sqrt{338} = \sqrt{169 \times 2} = 13\sqrt{2}$
4
A calculator, or long division of digits, gives
$\sqrt{338} \approx 18.384776$

LaTeX source of the formulas on this page

\[ \sqrt{338} = 13\sqrt{2} \approx 18.384776 \]
\[ \sqrt{338} = \sqrt{169 \times 2} = 13\sqrt{2} \]
\[ \sqrt{338} \approx 18.384776 \]

What is the square root of 338?

The square root of 338 is 18.384776 (rounded to 6 decimal places). In simplest radical form it is 13√2.

Is 338 a perfect square?

No. It lies between 18² = 324 and 19² = 361.

What is 338 squared?

338 × 338 = 114244.

What is the square root of 338 rounded to 2 decimals?

18.38.