# How do you find the square root of 8.2544?

Jul 31, 2017

$\sqrt{8.2544} \approx 2.873$

#### Explanation:

As $8.2544$ is not a complete square, let us use long division method for taking square root.

$\textcolor{w h i t e}{\times x} 2 \textcolor{w h i t e}{\times} .8 \textcolor{w h i t e}{\times} 7 \textcolor{w h i t e}{\times} 3$
$\underline{2} | \overline{8} . \textcolor{w h i t e}{.} \overline{25} \textcolor{w h i t e}{.} \overline{44} \textcolor{w h i t e}{.} \overline{00} \textcolor{w h i t e}{.} \overline{00}$
$\textcolor{w h i t e}{X X} \underline{4} \textcolor{w h i t e}{X} \downarrow$
$\textcolor{red}{4} 8 | \textcolor{w h i t e}{X} 4 \textcolor{w h i t e}{.} 25$
$\textcolor{w h i t e}{\times X x} \underline{3 \textcolor{w h i t e}{.} 84}$
$\textcolor{w h i t e}{x} \textcolor{red}{56} 7 | \textcolor{w h i t e}{X} 41 \textcolor{w h i t e}{.} 44$
$\textcolor{w h i t e}{\times \times \times} \underline{39 \textcolor{w h i t e}{.} 69}$
$\textcolor{w h i t e}{\times} \textcolor{red}{574} 3 | 1 \textcolor{w h i t e}{x} 75 \textcolor{w h i t e}{.} 00$
$\textcolor{w h i t e}{\times \times x . x} \underline{1 \textcolor{w h i t e}{.} 72 \textcolor{w h i t e}{.} 29}$
$\textcolor{w h i t e}{\times x} \textcolor{red}{11486} | \textcolor{w h i t e}{.} 2 \textcolor{w h i t e}{.} 71$

Hence $\sqrt{8.2544} \approx 2.873$