Square root of 1566

The square root of 1566 is 39.572718 (rounded to 6 decimal places). In simplest radical form it is 3√174.

Square root of 1566

Pick any whole number from 1 to 10,000.

\sqrt{1566} = 3\sqrt{174} \approx 39.572718

How to work it out

1
The square root of 1566 is the number that multiplied by itself gives 1566.
2
1566 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: 1566 = 9 × 174, so
$\sqrt{1566} = \sqrt{9 \times 174} = 3\sqrt{174}$
4
A calculator, or long division of digits, gives
$\sqrt{1566} \approx 39.572718$

LaTeX source of the formulas on this page

\[ \sqrt{1566} = 3\sqrt{174} \approx 39.572718 \]
\[ \sqrt{1566} = \sqrt{9 \times 174} = 3\sqrt{174} \]
\[ \sqrt{1566} \approx 39.572718 \]

What is the square root of 1566?

The square root of 1566 is 39.572718 (rounded to 6 decimal places). In simplest radical form it is 3√174.

Is 1566 a perfect square?

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

What is 1566 squared?

1566 × 1566 = 2452356.

What is the square root of 1566 rounded to 2 decimals?

39.57.