Square root of 423

The square root of 423 is 20.566964 (rounded to 6 decimal places). In simplest radical form it is 3√47.

Square root of 423

Pick any whole number from 1 to 10,000.

\sqrt{423} = 3\sqrt{47} \approx 20.566964

How to work it out

1
The square root of 423 is the number that multiplied by itself gives 423.
2
423 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: 423 = 9 × 47, so
$\sqrt{423} = \sqrt{9 \times 47} = 3\sqrt{47}$
4
A calculator, or long division of digits, gives
$\sqrt{423} \approx 20.566964$

LaTeX source of the formulas on this page

\[ \sqrt{423} = 3\sqrt{47} \approx 20.566964 \]
\[ \sqrt{423} = \sqrt{9 \times 47} = 3\sqrt{47} \]
\[ \sqrt{423} \approx 20.566964 \]

What is the square root of 423?

The square root of 423 is 20.566964 (rounded to 6 decimal places). In simplest radical form it is 3√47.

Is 423 a perfect square?

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

What is 423 squared?

423 × 423 = 178929.

What is the square root of 423 rounded to 2 decimals?

20.57.