Square root of 180

The square root of 180 is 13.416408 (rounded to 6 decimal places). In simplest radical form it is 6√5.

Square root of 180

Pick any whole number from 1 to 10,000.

\sqrt{180} = 6\sqrt{5} \approx 13.416408

How to work it out

1
The square root of 180 is the number that multiplied by itself gives 180.
2
180 is between the perfect squares 13² = 169 and 14² = 196, so its square root is between 13 and 14.
3
Pull out the biggest square factor: 180 = 36 × 5, so
$\sqrt{180} = \sqrt{36 \times 5} = 6\sqrt{5}$
4
A calculator, or long division of digits, gives
$\sqrt{180} \approx 13.416408$

LaTeX source of the formulas on this page

\[ \sqrt{180} = 6\sqrt{5} \approx 13.416408 \]
\[ \sqrt{180} = \sqrt{36 \times 5} = 6\sqrt{5} \]
\[ \sqrt{180} \approx 13.416408 \]

What is the square root of 180?

The square root of 180 is 13.416408 (rounded to 6 decimal places). In simplest radical form it is 6√5.

Is 180 a perfect square?

No. It lies between 13² = 169 and 14² = 196.

What is 180 squared?

180 × 180 = 32400.

What is the square root of 180 rounded to 2 decimals?

13.42.