Rozloz liczbe podpoerwiastkowa na czynnikipierwsze I wylacz czynnik przed znak pierwiastka..
A √540
B √448
C√864
D√972
E(3)√432
F(3)√1375
Zad wylacz czynnik przed znak pierwiastka I zapisz krocej
√12+5√3
2√20+√5
√18-2√8
√90+(3)√135
A √540
B √448
C√864
D√972
E(3)√432
F(3)√1375
Zad wylacz czynnik przed znak pierwiastka I zapisz krocej
√12+5√3
2√20+√5
√18-2√8
√90+(3)√135
basetla
![a) \ \ \ \sqrt{540} = \sqrt{36*15} = \sqrt{36}*\sqrt{15} = 6\sqrt{15}\\\\b) \ \ \ \sqrt{448} = \sqrt{64*7} = \sqrt{64}*\sqrt{7} = 8\sqrt{7}\\\\c) \ \ \ \sqrt{864} = \sqrt{144*6} = \sqrt{144}*\sqrt{6} = 12\sqrt{6}\\\\d) \ \ \ \sqrt{972}=\sqrt{324*3} = \sqrt{324}*\sqrt{3}=18\sqrt{3}\\\\e) \ \ \ \sqrt[3]{432} = \sqrt[3]{216*2} = \sqrt[3]{216}*\sqrt[3]{2}=6\sqrt[3]{2}\\\\f) \ \ \ \sqrt[3]{1375} = \sqrt[3]{125*3} = \sqrt[3]{125}*\sqrt[3]{3} = 5\sqrt[3]{3}](https://tex.z-dn.net/?f=a%29+%5C++%5C++%5C+%5Csqrt%7B540%7D+%3D+%5Csqrt%7B36%2A15%7D+%3D+%5Csqrt%7B36%7D%2A%5Csqrt%7B15%7D+%3D+6%5Csqrt%7B15%7D%5C%5C%5C%5Cb%29+%5C++%5C++%5C+%5Csqrt%7B448%7D+%3D+%5Csqrt%7B64%2A7%7D+%3D+%5Csqrt%7B64%7D%2A%5Csqrt%7B7%7D+%3D+8%5Csqrt%7B7%7D%5C%5C%5C%5Cc%29+%5C++%5C++%5C+%5Csqrt%7B864%7D+%3D+%5Csqrt%7B144%2A6%7D+%3D+%5Csqrt%7B144%7D%2A%5Csqrt%7B6%7D+%3D+12%5Csqrt%7B6%7D%5C%5C%5C%5Cd%29+%5C++%5C++%5C+%5Csqrt%7B972%7D%3D%5Csqrt%7B324%2A3%7D+%3D+%5Csqrt%7B324%7D%2A%5Csqrt%7B3%7D%3D18%5Csqrt%7B3%7D%5C%5C%5C%5Ce%29+%5C++%5C++%5C+%5Csqrt%5B3%5D%7B432%7D+%3D+%5Csqrt%5B3%5D%7B216%2A2%7D+%3D+%5Csqrt%5B3%5D%7B216%7D%2A%5Csqrt%5B3%5D%7B2%7D%3D6%5Csqrt%5B3%5D%7B2%7D%5C%5C%5C%5Cf%29+%5C++%5C++%5C+%5Csqrt%5B3%5D%7B1375%7D+%3D+%5Csqrt%5B3%5D%7B125%2A3%7D+%3D+%5Csqrt%5B3%5D%7B125%7D%2A%5Csqrt%5B3%5D%7B3%7D+%3D+5%5Csqrt%5B3%5D%7B3%7D "a) \ \ \ \sqrt{540} = \sqrt{36*15} = \sqrt{36}*\sqrt{15} = 6\sqrt{15}\\\\b) \ \ \ \sqrt{448} = \sqrt{64*7} = \sqrt{64}*\sqrt{7} = 8\sqrt{7}\\\\c) \ \ \ \sqrt{864} = \sqrt{144*6} = \sqrt{144}*\sqrt{6} = 12\sqrt{6}\\\\d) \ \ \ \sqrt{972}=\sqrt{324*3} = \sqrt{324}*\sqrt{3}=18\sqrt{3}\\\\e) \ \ \ \sqrt[3]{432} = \sqrt[3]{216*2} = \sqrt[3]{216}*\sqrt[3]{2}=6\sqrt[3]{2}\\\\f) \ \ \ \sqrt[3]{1375} = \sqrt[3]{125*3} = \sqrt[3]{125}*\sqrt[3]{3} = 5\sqrt[3]{3}")
![\sqrt{12}+5\sqrt{3}=\sqrt{4*3}+5\sqrt{3}=\sqrt{4}*\sqrt{3}+5\sqrt{3}=2\sqrt{3}+5\sqrt{3}=7\sqrt{3}\\\\2\sqrt{20}+\sqrt{5}=2\sqrt{4*5}+\sqrt{5}=2\sqrt{4}*\sqrt{5}+\sqrt{5}=4\sqrt{5}+\sqrt{5}=5\sqrt{5}\\\\\sqrt{18}-2\sqrt{8}=\sqrt{9*2}-2\sqrt{4*2} = \sqrt{9}*\sqrt{2}-2\sqrt{4}*\sqrt{2}=3\sqrt{2}-4\sqrt{2}=\\=-\sqrt{2}\\\\\sqrt{90}+\sqrt[3]{135} = \sqrt{9*10}+\sqrt[3]{27*5} = \sqrt{9}*\sqrt{10}+\sqrt[3]{27}*\sqrt[3]{5} = \\=3\sqrt{10}+3\sqrt[3]{5}=3(\sqrt{10}+\sqrt[3]{5})](https://tex.z-dn.net/?f=%5Csqrt%7B12%7D%2B5%5Csqrt%7B3%7D%3D%5Csqrt%7B4%2A3%7D%2B5%5Csqrt%7B3%7D%3D%5Csqrt%7B4%7D%2A%5Csqrt%7B3%7D%2B5%5Csqrt%7B3%7D%3D2%5Csqrt%7B3%7D%2B5%5Csqrt%7B3%7D%3D7%5Csqrt%7B3%7D%5C%5C%5C%5C2%5Csqrt%7B20%7D%2B%5Csqrt%7B5%7D%3D2%5Csqrt%7B4%2A5%7D%2B%5Csqrt%7B5%7D%3D2%5Csqrt%7B4%7D%2A%5Csqrt%7B5%7D%2B%5Csqrt%7B5%7D%3D4%5Csqrt%7B5%7D%2B%5Csqrt%7B5%7D%3D5%5Csqrt%7B5%7D%5C%5C%5C%5C%5Csqrt%7B18%7D-2%5Csqrt%7B8%7D%3D%5Csqrt%7B9%2A2%7D-2%5Csqrt%7B4%2A2%7D+%3D+%5Csqrt%7B9%7D%2A%5Csqrt%7B2%7D-2%5Csqrt%7B4%7D%2A%5Csqrt%7B2%7D%3D3%5Csqrt%7B2%7D-4%5Csqrt%7B2%7D%3D%5C%5C%3D-%5Csqrt%7B2%7D%5C%5C%5C%5C%5Csqrt%7B90%7D%2B%5Csqrt%5B3%5D%7B135%7D+%3D+%5Csqrt%7B9%2A10%7D%2B%5Csqrt%5B3%5D%7B27%2A5%7D+%3D+%5Csqrt%7B9%7D%2A%5Csqrt%7B10%7D%2B%5Csqrt%5B3%5D%7B27%7D%2A%5Csqrt%5B3%5D%7B5%7D+%3D+%5C%5C%3D3%5Csqrt%7B10%7D%2B3%5Csqrt%5B3%5D%7B5%7D%3D3%28%5Csqrt%7B10%7D%2B%5Csqrt%5B3%5D%7B5%7D%29 "\sqrt{12}+5\sqrt{3}=\sqrt{4*3}+5\sqrt{3}=\sqrt{4}*\sqrt{3}+5\sqrt{3}=2\sqrt{3}+5\sqrt{3}=7\sqrt{3}\\\\2\sqrt{20}+\sqrt{5}=2\sqrt{4*5}+\sqrt{5}=2\sqrt{4}*\sqrt{5}+\sqrt{5}=4\sqrt{5}+\sqrt{5}=5\sqrt{5}\\\\\sqrt{18}-2\sqrt{8}=\sqrt{9*2}-2\sqrt{4*2} = \sqrt{9}*\sqrt{2}-2\sqrt{4}*\sqrt{2}=3\sqrt{2}-4\sqrt{2}=\\=-\sqrt{2}\\\\\sqrt{90}+\sqrt[3]{135} = \sqrt{9*10}+\sqrt[3]{27*5} = \sqrt{9}*\sqrt{10}+\sqrt[3]{27}*\sqrt[3]{5} = \\=3\sqrt{10}+3\sqrt[3]{5}=3(\sqrt{10}+\sqrt[3]{5})")
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