Square root of 825

The square root of 825 is 28.722813 (rounded to 6 decimal places). In simplest radical form it is 5√33.

Square root of 825

Pick any whole number from 1 to 10,000.

\sqrt{825} = 5\sqrt{33} \approx 28.722813

How to work it out

1
The square root of 825 is the number that multiplied by itself gives 825.
2
825 is between the perfect squares 28² = 784 and 29² = 841, so its square root is between 28 and 29.
3
Pull out the biggest square factor: 825 = 25 × 33, so
$\sqrt{825} = \sqrt{25 \times 33} = 5\sqrt{33}$
4
A calculator, or long division of digits, gives
$\sqrt{825} \approx 28.722813$

LaTeX source of the formulas on this page

\[ \sqrt{825} = 5\sqrt{33} \approx 28.722813 \]
\[ \sqrt{825} = \sqrt{25 \times 33} = 5\sqrt{33} \]
\[ \sqrt{825} \approx 28.722813 \]

What is the square root of 825?

The square root of 825 is 28.722813 (rounded to 6 decimal places). In simplest radical form it is 5√33.

Is 825 a perfect square?

No. It lies between 28² = 784 and 29² = 841.

What is 825 squared?

825 × 825 = 680625.

What is the square root of 825 rounded to 2 decimals?

28.72.