given that: √2 = 1.414, √3 = 1.732, √5 = 2.236 and √7 = 2.646, evalute each of the following: √144/7

Question

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

(i) \(\sqrt{\frac{144}{7}}\)

(ii) \(\sqrt{\frac{2500}{3}}\)

Answer 1

(i) \(\sqrt{\frac{144}{7}}\) = \(\frac{\sqrt{12}\times\sqrt{12}}{\sqrt{7}}\)

 = \(\frac{12}{2.646}\)

 = 4.535

(ii) \(\sqrt{\frac{2500}{3}}\) = \(\frac{\sqrt{5}\times\sqrt{5}\times\sqrt{10}\times\sqrt{10}}{\sqrt{3}}\)

 = \(\frac{{5}\times{10}}{\sqrt{3}}\)

 = \(\frac{50}{1.732}\)

 = 28.867