Square root of 1540

The square root of 1540 is 39.242834 (rounded to 6 decimal places). In simplest radical form it is 2√385.

Square root of 1540

Pick any whole number from 1 to 10,000.

\sqrt{1540} = 2\sqrt{385} \approx 39.242834

How to work it out

1
The square root of 1540 is the number that multiplied by itself gives 1540.
2
1540 is between the perfect squares 39² = 1521 and 40² = 1600, so its square root is between 39 and 40.
3
Pull out the biggest square factor: 1540 = 4 × 385, so
$\sqrt{1540} = \sqrt{4 \times 385} = 2\sqrt{385}$
4
A calculator, or long division of digits, gives
$\sqrt{1540} \approx 39.242834$

LaTeX source of the formulas on this page

\[ \sqrt{1540} = 2\sqrt{385} \approx 39.242834 \]
\[ \sqrt{1540} = \sqrt{4 \times 385} = 2\sqrt{385} \]
\[ \sqrt{1540} \approx 39.242834 \]

What is the square root of 1540?

The square root of 1540 is 39.242834 (rounded to 6 decimal places). In simplest radical form it is 2√385.

Is 1540 a perfect square?

No. It lies between 39² = 1521 and 40² = 1600.

What is 1540 squared?

1540 × 1540 = 2371600.

What is the square root of 1540 rounded to 2 decimals?

39.24.