a)
Grupam termenii convenabil:
[tex]\sqrt{\frac{4}{9} } +\sqrt{\frac{49}{9} }-\sqrt{\frac{48}{45} } =\frac{2}{3}+\frac{7}{3}-\sqrt{\frac{16}{15} } =3-\frac{4}{\sqrt{15} } =3-\frac{4\sqrt{15} }{15} =\frac{45-4\sqrt{15} }{15}[/tex]
b)
Scoatem de sub radical:
[tex]\frac{10\sqrt{10} }{12\sqrt{2} } -\sqrt{20} +\frac{6\sqrt{5} }{16} =\\\\\frac{5\sqrt{5} }{6} -2\sqrt{5} +\frac{3\sqrt{5} }{8}[/tex]
Aducem la acelaasi numitor comun, 24
[tex]\frac{20\sqrt{5}-48\sqrt{5}+9\sqrt{5} }{24} =-\frac{19\sqrt{5} }{24}[/tex]
c)
Introducem intregii in fractie, iar 49 va iesi de sub radical:
[tex]\frac{\sqrt{219} }{7}+\frac{\sqrt{50} }{7}+ \frac{\sqrt{128} }{7} -\frac{\sqrt{162} }{7} =[/tex]
Scoatem de sub radical si obtinem:
[tex]\frac{\sqrt{219} +5\sqrt{2} +8\sqrt{2}-9\sqrt{2} }{7}[/tex]
[tex]\frac{\sqrt{219}+4\sqrt{2} }{7}[/tex]
d)
Introducem intregii in fractie si scoatem de sub radical numitorul:
[tex]\frac{\sqrt{108} }{10}- \frac{\sqrt{768} }{20} +\frac{\sqrt{588} }{4}-\frac{\sqrt{27} }{4} =[/tex]
Scoatem de sub radical si obtinem:
[tex]\frac{6\sqrt{3} }{10} -\frac{16\sqrt{3} }{20} +\frac{14\sqrt{3} -3\sqrt{3} }{4} =\\\\\frac{12\sqrt{3}-16\sqrt{3} +55\sqrt{3} }{20} =\frac{51\sqrt{3} }{20}[/tex]
Un alt exercitiu cu radicali gasesti aici: https://brainly.ro/tema/4746452
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