Square root of 414

The square root of 414 is 20.34699 (rounded to 6 decimal places). In simplest radical form it is 3√46.

Square root of 414

Pick any whole number from 1 to 10,000.

\sqrt{414} = 3\sqrt{46} \approx 20.34699

How to work it out

1
The square root of 414 is the number that multiplied by itself gives 414.
2
414 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: 414 = 9 × 46, so
$\sqrt{414} = \sqrt{9 \times 46} = 3\sqrt{46}$
4
A calculator, or long division of digits, gives
$\sqrt{414} \approx 20.34699$

LaTeX source of the formulas on this page

\[ \sqrt{414} = 3\sqrt{46} \approx 20.34699 \]
\[ \sqrt{414} = \sqrt{9 \times 46} = 3\sqrt{46} \]
\[ \sqrt{414} \approx 20.34699 \]

What is the square root of 414?

The square root of 414 is 20.34699 (rounded to 6 decimal places). In simplest radical form it is 3√46.

Is 414 a perfect square?

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

What is 414 squared?

414 × 414 = 171396.

What is the square root of 414 rounded to 2 decimals?

20.35.