7.
[tex]a) \\\sqrt{48}+2\sqrt{3} = \sqrt{16*3}+2\sqrt3=4\sqrt3+2\sqrt3=6\sqrt3\\\\b)\\\frac{\sqrt{125}-\sqrt{20}}{\sqrt5}=\frac{\sqrt{25*5}-\sqrt{4*5}}{\sqrt{5}} = \frac{5\sqrt5-2\sqrt5}{\sqrt5}=\frac{3\sqrt5}{\sqrt5}=3\\\\c)\\\sqrt[3]{375} + \sqrt[3]{-192}=\sqrt[3]{125*3}+\sqrt[3]{-64*3}=5\sqrt[3]{3}-4\sqrt[3]3=\sqrt[3]3[/tex]
8.
[tex]a = 3\sqrt7\\b = 2\sqrt{14}\\P=ab\\P = 3\sqrt7*2\sqrt{14} \\P = 6\sqrt{7*14}\\P = 6\sqrt{98} = 6\sqrt{49*2} = 6*7\sqrt2=42\sqrt2[/tex]
Odp. A
9.
Wynik dzialania [tex]\sqrt{20} * \sqrt{0,2}[/tex] jest liczba naturalna.
[tex]\sqrt{20}*\sqrt{0,2} = \sqrt{20*0.2} = \sqrt{4} = 2[/tex]
Prawda
Wynik dzialania [tex]\sqrt{75} + \sqrt{75}[/tex] jest liczba wymierna.
[tex]\sqrt{75}+\sqrt{75} = 2\sqrt{75}=2*5\sqrt{3} = 10\sqrt{3}[/tex]
Odp. Falsz
Wyrazenie [tex]\frac34\sqrt{0,08}[/tex] jest rowne [tex]\sqrt{\frac9{200}}[/tex]
[tex]\frac34\sqrt{0,08} = \frac34\sqrt{\frac8{100}} = \frac34*\frac{\sqrt{8}}{10} = \frac{3\sqrt{4*2}}{40} = \frac{6\sqrt2}{40} = \frac{3\sqrt2}{20}[/tex]
Falsz.
10.
[tex]\sqrt{1\frac79} * 3^3-(\frac13)^2=\sqrt{\frac{16}9} * 27-\frac{1}{9} = \frac{4}{3}*27-\frac19=4*9-\frac{1}{9} = 36-\frac19=35\frac89[/tex]
Odp. D
