Question

Is 1800 a perfect square? If not, find the smallest number by which it can be divided to make it a perfect square.

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{prime}\mathrm{factoristion}\mathrm{of}1800\mathrm{is}: \\ 1800=\underline{2\times 2}\times 2\times \underline{3\times 3}\times \underline{5\times 5} \\ \mathrm{Here},\mathrm{prime}\mathrm{factor}2\mathrm{does}\mathrm{not}\mathrm{ocurr}\mathrm{in}\mathrm{a}\mathrm{pair},\mathrm{so}1800\mathrm{is}\mathrm{not}\mathrm{a}\mathrm{perfect}\mathrm{square}. \\ \mathrm{Now},\mathrm{to}\mathrm{make}1800\mathrm{a}\mathrm{perfect}\mathrm{square},\mathrm{it}\mathrm{must}\mathrm{be}\mathrm{divided}\mathrm{by}2. \\ \mathrm{Now},1800÷2=\frac{2\times 2\times 2\times 3\times 3\times 5\times 5}{2}=900\left(\mathrm{a}\mathrm{perfect}\mathrm{square}\mathrm{number}\right) \\ \mathrm{Now},900=\underline{2\times 2}\times \underline{3\times 3}\times \underline{5\times 5} \\ \sqrt{900}=\sqrt{\underline{2\times 2}\times \underline{3\times 3}\times \underline{5\times 5}}=2\times 3\times 5=30 \end{gathered}$$