Odpowiedź:
zad 1
[tex]a) \: \: \sqrt{49} - \sqrt[3]{ - 27} = 7 - ( - 3) = 10 \\ b) \: \: 5 \sqrt{\frac{1}{100}} + \frac{ \sqrt{121} }{4} = 5 \frac{1}{10} + \frac{11}{4} = 5 \frac{2}{20} + \frac{55}{20 = 5 \frac{57}{20} } = 7 \frac{17}{20} [/tex]
[tex] c) \: \: \sqrt[3]{36 \times \sqrt{36} } = \sqrt[3]{36 \times 6} = 6 \\ d) \: \: \sqrt{3 \sqrt{3 \sqrt{9} } } = \sqrt{3 \sqrt{3 \times 3} } = \sqrt{3 \times 3} = 3[/tex]
[tex]e) \: \: \sqrt{16} + \sqrt{9} - \sqrt{16 + 9} = 4 + 3 - \sqrt{25} = 7 - 5 = 2 \\ f) \: \: \sqrt{400} \div \sqrt[3]{8} + \sqrt{25} = 20 \div 2 + 5 = 15[/tex]
zad.2
[tex]a) \: \: \frac{15 \sqrt{13} }{5 \sqrt{13} } = 3 \\ b) \: \: 4 \sqrt{2} + 7 \sqrt{2} = 11 \sqrt{2} \\ c) \: \: \frac{12 + 10 \sqrt[3]{4} }{2} = \frac{2(6 + 5 \sqrt[3]{4}) }{2} = 6 + 5 \sqrt[3]{4} \\ d) \: \: 3 \sqrt[3]{3} + 4 \sqrt[3]{3} + 5 \sqrt[3]{ - 3} = 7 \sqrt[3]{3} + ( - 5 \sqrt[3]{3} ) = 2 \sqrt[3]{3} [/tex]
zad.3
[tex]a) \: \: 5( \sqrt{3} {)}^{2} = 5 \times 3 = 15 \\ b) \: \: 4 \sqrt{6} \times 2 \sqrt{6} = 4 \times 2 \times \sqrt{6} \times \sqrt{6 } = 48 \\ c) \: \: ( \frac{2}{5} \sqrt{15} {)}^{2} = \frac{4}{25} \times 15 = \frac{12}{5} = 2 \frac{2}{5} [/tex]
zad.4
[tex]a) \: \: 4 \sqrt{7} - 5 - 7 \sqrt{7} + 8 = 3 - 3 \sqrt{7} = 3(1 - \sqrt{7} ) \\ b) \: \: 4(5 + 3 \sqrt{3} ) - 2(4 + 5 \sqrt{3} ) = 20 + 12 \sqrt{3} - 8 - 10 \sqrt{3} = 12 + 2 \sqrt{3} = 2(6 + \sqrt{3} ) \\ c) \: \: 5( \sqrt[3]{10} - 2) - 3( \sqrt[3]{10} - 4) = 5 \sqrt[3]{10} - 10 - 3 \sqrt[3]{10} + 12 = 2 \sqrt[3]{10} + 2
[/tex]
zad.5
[tex]a) \: \: \sqrt{7} (5 - \sqrt{7} ) = 5 \sqrt{7} - 7 \\ b) \: \: (3 - \sqrt{5} )(5 + 2 \sqrt{5} = 15 + 6 \sqrt{5} - 5 \sqrt{5} - 10 = 5 + \sqrt{5} [/tex]
zad.6
[tex]a) \: \: \frac{1}{4} ( \sqrt[3]{12} {)}^{3} = \frac{1}{4} \times 12 = 3 \\ b) \: \: 2 \sqrt[3]{7} \times 3( \sqrt[3]{7} {)}^{2} = 2 \sqrt[3]{7} \times 3 \sqrt[3]{ {7}^{2} } = 2 \times 3 \times 7 = 42 \\ c) \: \: ( - 5 \sqrt[3]{ - 3} {)}^{2} \times \sqrt[3]{ - 3} = 25 \times ( - 3) = - 75[/tex]
zad.7
[tex]a) \: \: 3 \sqrt{2} \times \sqrt{5} = 3 \sqrt{10} \\ b) \: \: \frac{4 \sqrt{15} }{2 \sqrt{5} } = 2 \sqrt{3} \\ c) \: \: 3 \sqrt[3]{6} \times \sqrt[3]{2} = 3 \sqrt[3]{12} \\ d) \: \: \frac{15 \sqrt[3]{ - 6} }{3 \sqrt[3]{3} } = 5 \sqrt[3]{ - 2} [/tex]
zad.8
[tex]a) \: \: \sqrt{20} = \sqrt{4 \times 5} = 2 \sqrt{5} \\ b) \: \: \sqrt{ {2}^{5} } = \sqrt{32} = \sqrt{16 \times 2} = 4 \sqrt{2} \\ c) \: \: \sqrt[3]{56} = \sqrt[3]{8 \times 7} = 2 \sqrt[3]{7} \\ d) \: \: \sqrt[3]{ {3}^{5} } = 3 \sqrt[3]{ {3}^{2} } [/tex]
