Square root of 1408

The square root of 1408 is 37.523326 (rounded to 6 decimal places). In simplest radical form it is 8√22.

Square root of 1408

Pick any whole number from 1 to 10,000.

\sqrt{1408} = 8\sqrt{22} \approx 37.523326

How to work it out

1
The square root of 1408 is the number that multiplied by itself gives 1408.
2
1408 is between the perfect squares 37² = 1369 and 38² = 1444, so its square root is between 37 and 38.
3
Pull out the biggest square factor: 1408 = 64 × 22, so
$\sqrt{1408} = \sqrt{64 \times 22} = 8\sqrt{22}$
4
A calculator, or long division of digits, gives
$\sqrt{1408} \approx 37.523326$

LaTeX source of the formulas on this page

\[ \sqrt{1408} = 8\sqrt{22} \approx 37.523326 \]
\[ \sqrt{1408} = \sqrt{64 \times 22} = 8\sqrt{22} \]
\[ \sqrt{1408} \approx 37.523326 \]

What is the square root of 1408?

The square root of 1408 is 37.523326 (rounded to 6 decimal places). In simplest radical form it is 8√22.

Is 1408 a perfect square?

No. It lies between 37² = 1369 and 38² = 1444.

What is 1408 squared?

1408 × 1408 = 1982464.

What is the square root of 1408 rounded to 2 decimals?

37.52.