Square root of 117

The square root of 117 is 10.816654 (rounded to 6 decimal places). In simplest radical form it is 3√13.

Square root of 117

Pick any whole number from 1 to 10,000.

\sqrt{117} = 3\sqrt{13} \approx 10.816654

How to work it out

1
The square root of 117 is the number that multiplied by itself gives 117.
2
117 is between the perfect squares 10² = 100 and 11² = 121, so its square root is between 10 and 11.
3
Pull out the biggest square factor: 117 = 9 × 13, so
$\sqrt{117} = \sqrt{9 \times 13} = 3\sqrt{13}$
4
A calculator, or long division of digits, gives
$\sqrt{117} \approx 10.816654$

LaTeX source of the formulas on this page

\[ \sqrt{117} = 3\sqrt{13} \approx 10.816654 \]
\[ \sqrt{117} = \sqrt{9 \times 13} = 3\sqrt{13} \]
\[ \sqrt{117} \approx 10.816654 \]

What is the square root of 117?

The square root of 117 is 10.816654 (rounded to 6 decimal places). In simplest radical form it is 3√13.

Is 117 a perfect square?

No. It lies between 10² = 100 and 11² = 121.

What is 117 squared?

117 × 117 = 13689.

What is the square root of 117 rounded to 2 decimals?

10.82.