[tex]a)~~3\sqrt{5} +4\sqrt{5} =7\sqrt{5} \\\\b)~~\sqrt{33} \cdot \sqrt{3\frac{2}{3} } =\sqrt{33} \cdot \sqrt{\frac{11}{3} } =\sqrt{3\cdot \frac{11}{3} }=\sqrt{11} \\\\c)~~\sqrt{300} -7\sqrt{3} =\sqrt{100\cdot 3} -7\sqrt{3} =\sqrt{10^{2}\cdot 3 } -7\sqrt{3} =10\sqrt{3} -7\sqrt{3} =3\sqrt{3} \\\\d)~~3\sqrt{6} \cdot \dfrac{1}{2} \sqrt{2} =3\cdot \dfrac{1}{2} \sqrt{6\cdot 2} =\dfrac{3}{2} \sqrt{12} =\dfrac{3}{2} \sqrt{4\cdot 3} =\dfrac{3}{2} \sqrt{2^{2}\cdot 3 } =\dfrac{3}{2}\cdot 2 \sqrt{3} =3\sqrt{3} \\[/tex]
[tex]e)~~(\dfrac{4\sqrt{6} }{3} )^{2} =\dfrac{4^{2}\cdot (\sqrt{6}) ^{2} }{3^{2} } =\dfrac{16\cdot 6}{9} =\dfrac{32}{3} =10\dfrac{2}{3}[/tex]
korzystam ze wzorów:
[tex]\sqrt[n]{x} \cdot \sqrt[n]{y} =\sqrt[n]{x\cdot y} \\\\(\sqrt[n]{x} )^{n} =(x^{\frac{1}{n} }) ^{n} =x^{n\cdot \frac{1}{n} } =x\\\\a\sqrt{x} +b\sqrt{x} =(a+b)\sqrt{x} \\\\a\sqrt{x} -b\sqrt{x} =(a-b)\sqrt{x}[/tex]
