Square root of 8192

The square root of 8192 is 90.509668 (rounded to 6 decimal places). In simplest radical form it is 64√2.

Square root of 8192

Pick any whole number from 1 to 10,000.

\sqrt{8192} = 64\sqrt{2} \approx 90.509668

How to work it out

1
The square root of 8192 is the number that multiplied by itself gives 8192.
2
8192 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: 8192 = 4096 × 2, so
$\sqrt{8192} = \sqrt{4096 \times 2} = 64\sqrt{2}$
4
A calculator, or long division of digits, gives
$\sqrt{8192} \approx 90.509668$

LaTeX source of the formulas on this page

\[ \sqrt{8192} = 64\sqrt{2} \approx 90.509668 \]
\[ \sqrt{8192} = \sqrt{4096 \times 2} = 64\sqrt{2} \]
\[ \sqrt{8192} \approx 90.509668 \]

What is the square root of 8192?

The square root of 8192 is 90.509668 (rounded to 6 decimal places). In simplest radical form it is 64√2.

Is 8192 a perfect square?

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

What is 8192 squared?

8192 × 8192 = 67108864.

What is the square root of 8192 rounded to 2 decimals?

90.51.