Square root of 404

The square root of 404 is 20.099751 (rounded to 6 decimal places). In simplest radical form it is 2√101.

Square root of 404

Pick any whole number from 1 to 10,000.

\sqrt{404} = 2\sqrt{101} \approx 20.099751

How to work it out

1
The square root of 404 is the number that multiplied by itself gives 404.
2
404 is between the perfect squares 20² = 400 and 21² = 441, so its square root is between 20 and 21.
3
Pull out the biggest square factor: 404 = 4 × 101, so
$\sqrt{404} = \sqrt{4 \times 101} = 2\sqrt{101}$
4
A calculator, or long division of digits, gives
$\sqrt{404} \approx 20.099751$

LaTeX source of the formulas on this page

\[ \sqrt{404} = 2\sqrt{101} \approx 20.099751 \]
\[ \sqrt{404} = \sqrt{4 \times 101} = 2\sqrt{101} \]
\[ \sqrt{404} \approx 20.099751 \]

What is the square root of 404?

The square root of 404 is 20.099751 (rounded to 6 decimal places). In simplest radical form it is 2√101.

Is 404 a perfect square?

No. It lies between 20² = 400 and 21² = 441.

What is 404 squared?

404 × 404 = 163216.

What is the square root of 404 rounded to 2 decimals?

20.10.