Question

Write the simplest form of rationalising factor for the given surds.

(i) $\sqrt{32}\left(\mathrm{ii}\right)\sqrt{50}\left(\mathrm{iii}\right)\sqrt{27}\left(\mathrm{iv}\right)\frac{3}{5}\sqrt{10}\left(\mathrm{v}\right)3\sqrt{72}\left(\mathrm{vi}\right)4\sqrt{11}$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\mathrm{Since},\sqrt{32}=\sqrt{16\times 2}=4\sqrt{2} \\ \mathrm{So},\sqrt{2}\mathrm{is}\mathrm{the}\mathrm{simplest}\mathrm{form}\mathrm{of}\mathrm{rationalising}\mathrm{factor}. \end{gathered}$$

$$\begin{gathered} \left(\mathrm{ii}\right)\mathrm{Since},\sqrt{50}=\sqrt{25\times 2}=5\sqrt{2} \\ \mathrm{So},\sqrt{2}\mathrm{is}\mathrm{the}\mathrm{simplest}\mathrm{form}\mathrm{of}\mathrm{rationalising}\mathrm{factor}. \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iii}\right)\mathrm{Since},\sqrt{27}=\sqrt{9\times 3}=3\sqrt{3} \\ \mathrm{So},\sqrt{3}\mathrm{is}\mathrm{the}\mathrm{simplest}\mathrm{form}\mathrm{of}\mathrm{rationalising}\mathrm{factor}. \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iv}\right)\mathrm{Since},\frac{3}{5}\sqrt{10}=\frac{3}{5}\sqrt{2\times 5} \\ \mathrm{So},\sqrt{10}\mathrm{is}\mathrm{the}\mathrm{simplest}\mathrm{form}\mathrm{of}\mathrm{rationalising}\mathrm{factor}. \end{gathered}$$

$$\begin{gathered} \left(\mathrm{v}\right)\mathrm{Since},3\sqrt{72}=3\sqrt{36\times 2}=3\times 6\sqrt{2}=18\sqrt{2} \\ \mathrm{So},\sqrt{2}\mathrm{is}\mathrm{the}\mathrm{simplest}\mathrm{form}\mathrm{of}\mathrm{rationalising}\mathrm{factor}. \end{gathered}$$

$$\begin{gathered} \left(\mathrm{vi}\right)\mathrm{Since},4\sqrt{11}=4\sqrt{11\times 1} \\ \mathrm{So},\sqrt{11}\mathrm{is}\mathrm{the}\mathrm{simplest}\mathrm{form}\mathrm{of}\mathrm{rationalising}\mathrm{factor}. \end{gathered}$$