Question

Answer 1

a: \(\frac{\sqrt5-\sqrt3}{\sqrt2}=\frac{\sqrt2\left(\sqrt5-\sqrt3\right)}{2}=\frac{\sqrt{10}-\sqrt6}{2}\)

b: \(\frac{26}{5-2\sqrt3}=\frac{26\left(5+2\sqrt3\right)}{\left(5-2\sqrt3\right)\left(5+2\sqrt3\right)}\)

\(=\frac{26\left(5+2\sqrt3\right)}{25-12}=2\left(5+2\sqrt3\right)=10+4\sqrt3\)

c: \(\frac{2\sqrt{10}-5}{4-\sqrt{10}}=\frac{\sqrt5\left(2\sqrt2-\sqrt5\right)}{\sqrt2\left(2\sqrt2-\sqrt5\right)}=\frac{\sqrt5}{\sqrt2}=\frac{\sqrt{10}}{2}\)

d: \(\frac{9-2\sqrt3}{3\sqrt6-2\sqrt2}=\frac{\sqrt3\left(3\sqrt3-2\right)}{\sqrt2\left(3\sqrt3-2\right)}=\sqrt{\frac32}=\frac{\sqrt6}{2}\)