Square root of 208

The square root of 208 is 14.422205 (rounded to 6 decimal places). In simplest radical form it is 4√13.

Square root of 208

Pick any whole number from 1 to 10,000.

\sqrt{208} = 4\sqrt{13} \approx 14.422205

How to work it out

1
The square root of 208 is the number that multiplied by itself gives 208.
2
208 is between the perfect squares 14² = 196 and 15² = 225, so its square root is between 14 and 15.
3
Pull out the biggest square factor: 208 = 16 × 13, so
$\sqrt{208} = \sqrt{16 \times 13} = 4\sqrt{13}$
4
A calculator, or long division of digits, gives
$\sqrt{208} \approx 14.422205$

LaTeX source of the formulas on this page

\[ \sqrt{208} = 4\sqrt{13} \approx 14.422205 \]
\[ \sqrt{208} = \sqrt{16 \times 13} = 4\sqrt{13} \]
\[ \sqrt{208} \approx 14.422205 \]

What is the square root of 208?

The square root of 208 is 14.422205 (rounded to 6 decimal places). In simplest radical form it is 4√13.

Is 208 a perfect square?

No. It lies between 14² = 196 and 15² = 225.

What is 208 squared?

208 × 208 = 43264.

What is the square root of 208 rounded to 2 decimals?

14.42.