Question

a, \(\sqrt{\frac{1}{60}}\) b, \(\frac{3-\sqrt{5}}{\sqrt{2}}\)

c, \(\frac{1}{2-\sqrt{3}}\)

d, \(\frac{3}{\sqrt{2}+\sqrt{5}}\)

e, \(\frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}}\)

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Answer 1

a, \(\sqrt{\frac{1}{60}}=\frac{\sqrt{1}}{\sqrt{60}}=\frac{\sqrt{1}.\sqrt{60}}{\sqrt{60}.\sqrt{60}}=\frac{\sqrt{60}}{60}=\frac{2.\sqrt{15}}{2.30}=\frac{\sqrt{15}}{30}\)

c, \(\frac{1}{2-\sqrt{3}}=\frac{2+\sqrt{3}}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}=\frac{2+\sqrt{3}}{4-3}=2+\sqrt{3}\)

d, \(\frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}}=\frac{\left(\sqrt{7}-\sqrt{3}\right)^2}{\left(\sqrt{7}+\sqrt{3}\right)\left(\sqrt{7}-\sqrt{3}\right)}=\frac{7-2\sqrt{21}+3}{7-3}=\frac{10-2\sqrt{21}}{4}\)