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Given that:\(\sqrt{2} = 1.414, \sqrt{3} = 1.732,\sqrt{5} = 2.236\) and \(\sqrt{7} = 2.646,\) and square roots of the following:

(i) \(\frac{169}{75}\)

(ii) \(\frac{400}{63}\)

(iii) \(\frac{150}{7}\)

(iv) \(\frac{256}{5}\)

(v) \(\frac{276}{50}\)

1 Answer

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(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

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