Zadanie 7
Usuń niewymierność z mianownika.
a)
\frac{3\sqrt7}{2\sqrt3}=\frac{3\sqrt7*\sqrt3}{2\sqrt3*\sqrt3}=\frac{\not3^1\sqrt{21}}{2*\not3^1}=\frac{\sqrt{21}}{2}
b)
\frac{\sqrt3-\sqrt{13}}{3\sqrt{13}}=\frac{(\sqrt3-\sqrt{13})*\sqrt{13}}{3\sqrt{13}*\sqrt{13}}=\frac{\sqrt{39}-13}{3*13}=\frac{\sqrt{39}-13}{39}
c)
\frac{3}{4-\sqrt3}=\frac{3(4+\sqrt3)}{(4-\sqrt3)(4+\sqrt3)}=\frac{3(4+\sqrt3)}{16-3}=\frac{3(4+\sqrt3)}{13}
d)
\frac{3\sqrt3+2\sqrt5}{3\sqrt5-2\sqrt2}=\frac{(3\sqrt3+2\sqrt5)(3\sqrt5+2\sqrt2)}{(3\sqrt5-2\sqrt2)(3\sqrt5+2\sqrt2)}=\frac{9\sqrt{15}+6\sqrt6+6*5+4\sqrt{10}}{9*5-4*2}=
=\frac{9\sqrt{15}+4\sqrt{10}+6\sqrt6+30}{37}