Question

Answer 1

a, \(\dfrac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}=\dfrac{\sqrt{5}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}=\sqrt{5}\)

Answer 2

b, \(\dfrac{\sqrt{7}-7}{\sqrt{7}-1}=\dfrac{-\sqrt{7}\left(\sqrt{7}-1\right)}{\sqrt{7}-1}=-\sqrt{7}\)

Answer 3

c, \(\dfrac{2\sqrt{5}-5\sqrt{2}}{\sqrt{5}-\sqrt{2}}=\dfrac{-\sqrt{10}\left(\sqrt{5}-\sqrt{2}\right)}{\sqrt{5}-\sqrt{2}}=-\sqrt{10}\)

Answer 4

e, \(\dfrac{5}{\sqrt{2}+\sqrt{7}}=\dfrac{5\left(\sqrt{7}-\sqrt{2}\right)}{\left(\sqrt{7}+\sqrt{2}\right)\left(\sqrt{7}-\sqrt{2}\right)}=\dfrac{5\left(\sqrt{7}-\sqrt{2}\right)}{7-2}=\sqrt{7}-\sqrt{2}\)

Answer 5

f, \(\dfrac{14-6\sqrt{5}}{3-\sqrt{5}}=\dfrac{\left(3-\sqrt{5}\right)^2}{3-\sqrt{5}}=3-\sqrt{5}\)

Answer 6

d, \(\dfrac{8}{\sqrt{5}-1}=\dfrac{8\left(\sqrt{5}+1\right)}{\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)}=\dfrac{8\left(\sqrt{5}+1\right)}{5-1}=2\sqrt{5}+2\)