Odpowiedź:
zad.9
[tex]a) \: 6 \sqrt{5} \times \sqrt{5} = 6 \times \sqrt{5} \times \sqrt{5} = 6 \times 5 = 30 \\ b) \: \sqrt{6} \times 4 \sqrt{6} = 4 \times \sqrt{6} \times \sqrt{6} = 4 \times 6 = 24 \\ c) \: \sqrt{7} \times 2 \sqrt{7} = 2 \times \sqrt{7} \times \sqrt{7} = 2 \times 7 = 14 \\ d) \: 2 \sqrt{3} \times 5 \sqrt{3} = 2 \times 5 \times \sqrt{3} \times \sqrt{3} = 10 \times 3 = 30 \\ e) \: - 4 \sqrt{2} \times 3 \sqrt{2} = - 4 \times 3 \times \sqrt{2} \times \sqrt{2} = - 12 \times 2 = - 24 \\ f) \: - 3 \sqrt{5} \times 2 \sqrt{5} = - 3 \times 2 \times \sqrt{5} \times \sqrt{5} = - 6 \times 5 = - 30[/tex]
zad.10
[tex]a) \: (4 \sqrt{5} {)}^{2} = {4}^{2} \times ( \sqrt{5} {)}^{2} = 16 \times 5 = 80 \\ b) \: (2 \sqrt{6 } {)}^{2} = {2}^{2} \times ( \sqrt{6} {)}^{2} = 4 \times 6 = 24 \\ c) \: ( \frac{ \sqrt{7} }{3} {)}^{2} = \frac{( \sqrt{7} {)}^{2} }{ {3}^{2} } = \frac{7}{9} \\ d) \: ( \frac{3 \sqrt{8} }{2} {)}^{2} = \frac{(3 \sqrt{8} {)}^{2} }{ {2}^{2} } = \frac{ {3}^{2} \times ( \sqrt{8 }{)}^{2} }{4} = \frac{9 \times 8}{4} = 18 \\ e) \: ( \frac{6}{ \sqrt{3} } {)}^{2} = \frac{ {6}^{2} }{( \sqrt{3} {)}^{2} } = \frac{36}{3} = 12 \\ f) \: ( \frac{3}{2 \sqrt{6} } {)}^{2} = \frac{ {3}^{2} }{(2 \sqrt{6} {)}^{2} } = \frac{9}{ {2}^{2} \times ( \sqrt{6} {)}^{2} } = \frac{9}{4 \times 6} = \frac{9}{36} = \frac{1}{4} [/tex]
