Square root of 420

The square root of 420 is 20.493902 (rounded to 6 decimal places). In simplest radical form it is 2√105.

Square root of 420

Pick any whole number from 1 to 10,000.

\sqrt{420} = 2\sqrt{105} \approx 20.493902

How to work it out

1
The square root of 420 is the number that multiplied by itself gives 420.
2
420 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: 420 = 4 × 105, so
$\sqrt{420} = \sqrt{4 \times 105} = 2\sqrt{105}$
4
A calculator, or long division of digits, gives
$\sqrt{420} \approx 20.493902$

LaTeX source of the formulas on this page

\[ \sqrt{420} = 2\sqrt{105} \approx 20.493902 \]
\[ \sqrt{420} = \sqrt{4 \times 105} = 2\sqrt{105} \]
\[ \sqrt{420} \approx 20.493902 \]

What is the square root of 420?

The square root of 420 is 20.493902 (rounded to 6 decimal places). In simplest radical form it is 2√105.

Is 420 a perfect square?

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

What is 420 squared?

420 × 420 = 176400.

What is the square root of 420 rounded to 2 decimals?

20.49.