Square root of 8144

The square root of 8144 is 90.244113 (rounded to 6 decimal places). In simplest radical form it is 4√509.

Square root of 8144

Pick any whole number from 1 to 10,000.

\sqrt{8144} = 4\sqrt{509} \approx 90.244113

How to work it out

1
The square root of 8144 is the number that multiplied by itself gives 8144.
2
8144 is between the perfect squares 90² = 8100 and 91² = 8281, so its square root is between 90 and 91.
3
Pull out the biggest square factor: 8144 = 16 × 509, so
$\sqrt{8144} = \sqrt{16 \times 509} = 4\sqrt{509}$
4
A calculator, or long division of digits, gives
$\sqrt{8144} \approx 90.244113$

LaTeX source of the formulas on this page

\[ \sqrt{8144} = 4\sqrt{509} \approx 90.244113 \]
\[ \sqrt{8144} = \sqrt{16 \times 509} = 4\sqrt{509} \]
\[ \sqrt{8144} \approx 90.244113 \]

What is the square root of 8144?

The square root of 8144 is 90.244113 (rounded to 6 decimal places). In simplest radical form it is 4√509.

Is 8144 a perfect square?

No. It lies between 90² = 8100 and 91² = 8281.

What is 8144 squared?

8144 × 8144 = 66324736.

What is the square root of 8144 rounded to 2 decimals?

90.24.