(i) \(\frac{169}{75}\)
\(\frac{169}{75} \) = \(\sqrt{\frac{169}{75}}\)
= \(\frac{\sqrt{13}\times\sqrt{13}}{\sqrt{5}\times\sqrt{5}\times\sqrt{3}}\)
= \(\frac{13}{5\sqrt{3}}\)
= \(\frac{13}{5(1.732)}\)
= \(\frac{13}{8.66}\)
= 1.50
(ii) \(\frac{400}{63}\)
\(\frac{400}{63} = \) \(\sqrt{\frac{400}{63}}\)
= \(\frac{\sqrt{2}\times\sqrt{2}\times{10}\times{10}}{\sqrt{3}\times\sqrt{3}\times\sqrt{7}}\)
= \(\frac{2\times{10}}{3\sqrt{7}}\)
= \(\frac{20}{3(2.646)}\)
= 2.519
(iii) \(\frac{150}{7}\)
\(\frac{150}{7}\) = \(\sqrt{\frac{150}{7}}\)
= \(\frac{\sqrt{3\times5\times5\times2}}{\sqrt{7}}\)
= \(\frac{5\sqrt3\times\sqrt{2}}{\sqrt{7}}\)
= \(\frac{5\times{1.731}{\times1.414}}{2.646}\)
= \(\frac{12.24524}{2.646}\)
= 4.627
(iv) \(\frac{256}{5}\)
\(\frac{256}{7} = \sqrt{\frac{256}{7}}\)
= \(\frac{\sqrt{16}\times\sqrt{16}}{\sqrt{5}}\)
= \(\frac{16}{\sqrt{5}}\)
= \(\frac{16}{2.236}\)
= 7.155
(v) \(\frac{276}{50}\)
\(\frac{276}{50}
\) = \(\sqrt{\frac{276}{50}}\)
= \(\frac{\sqrt{2\times2\times3\times23}}{\sqrt{5}\times\sqrt{5}\times\sqrt{2}}\)
= \(\frac{2\times\sqrt{3}\times\sqrt{23}}{5\sqrt{2}}\)
= \(\frac{2\times1.732\times4.796}{5(1.414)}\)
= 0.735