Question

Find the smallest number by which the number 3645 should be divided so as to get a perfect square. Also find the square root of the square numbers so obtained. [4 MARKS]

Answer 1

Concept : 1 Mark
Prime factorisation : 2 Marks
Conclusion : 1 Mark

$\begin{array}{cc}3& 3645\\ 3& 1215\\ 3& 405\\ 3& 135\\ 3& 45\\ 3& 15\\ 5& 5\\ & 1\end{array}$


$\therefore 3645=3\times 3\times 3\times 3\times 3\times 3\times 5$

$\therefore$ We have to divide 3645 by 5 to get, $3\times 3\times 3\times 3\times 3\times 3$

$i.e,\frac{3645}{5}=729$

$=\underset{–}{3\times 3}\times \underset{–}{3\times 3}\times \underset{–}{3\times 3}$

$\sqrt{729}=3\times 3\times 3=27$