Question

Find the square root of the following rational numbers.
$\frac{144}{441}$

Answer 1

$\begin{array}{cc}2& 144\\ 2& 72\\ 2& 36\\ 2& 18\\ 3& 9\\ 3& 3\\ & 1\end{array}$

$\sqrt{144}=\sqrt{(2\times 2)\times (2\times 2)\times (3\times 3)}$

$\Rightarrow \sqrt{144}=2\times 2\times 3$

$\Rightarrow \sqrt{144}=12$ ---(1)

$\begin{array}{cc}3& 441\\ 3& 147\\ 7& 49\\ 7& 7\\ & 1\end{array}$

$\Rightarrow \sqrt{441}=\sqrt{3\times 3)\times (7\times 7)}$

$\Rightarrow \sqrt{441}=3\times 7$

$\Rightarrow \sqrt{441}=21$ ---(2)

Let evaluate, $\sqrt{\frac{144}{441}}$

$\sqrt{\frac{144}{441}}$

$=\frac{\sqrt{144}}{\sqrt{441}}$

$=\frac{12}{21}$

$=\frac{4}{7}$

$\therefore \sqrt{\frac{144}{441}}=\frac{4}{7}$