Odpowiedzi #
1.4.4 #
a) $ (\sqrt{3} + \sqrt{6})^2 = (\sqrt{3})^2 + 2 \cdot \sqrt{3} \cdot \sqrt{6} + (\sqrt{6})^2 = 3 + 2\sqrt{18} + 6 = 9 + 2\sqrt{9\cdot2} = $ $ = 9 + 2\sqrt{9}\sqrt{2} = 9 + 2\cdot{3}\cdot\sqrt{2} = 9 + 6\sqrt{2}$
b) $(7 - 13^{\frac{1}{2}})^{\frac{1}{2}} \cdot (7 - 13^{\frac{1}{2}})^{\frac{1}{2}} = [(7 - 13^{\frac{1}{2}})(7 - 13^{\frac{1}{2}})]^{\frac{1}{2}} = [7^2 - (13^{\frac{1}{2}})^2]^{\frac{1}{2}} = (49-13)^{\frac{1}{2}}= $ $ =\sqrt{36} = 6$