Odpowiedź:
26) [tex]\sqrt{25 a^4} = \sqrt{25} *\sqrt{a^4} = 5 a^2[/tex] bo ( 5 a²)² = 25 [tex]a^4[/tex]
27) [tex]\sqrt{b^{18}} = b^9[/tex] ([tex]b^9)^2 = b^{9*2} = b^{18}[/tex]
28 ) [tex]\sqrt[3]{216 x^9 y^3} = 6 x^3 y[/tex] ( 6 [tex]x^3 y)^3 = 6^3*(x^3)^3*y^3 = 216 x^9 y^3[/tex]
29) [tex]\sqrt{\frac{64x^2}{y^{10}} } = \frac{8x}{y^5}[/tex] ( [tex]\frac{8x}{y^5} )^2=\frac{64x^2}{y^{10}}[/tex]
30) 2[tex]\sqrt{5*4\sqrt{3} } = 8 \sqrt{5*3} = 8 \sqrt{15}[/tex]
31) [tex]\frac{5\sqrt{3}*6\sqrt{2} }{10\sqrt{10} } = \frac{5*2*3\sqrt{6} }{10\sqrt{10} } =\frac{3\sqrt{6} }{\sqrt{10} } = 3\sqrt{0,6}[/tex]
32 ) 7[tex]\sqrt[3]{4} *5\sqrt[3]{3} = 4=35\sqrt[3]{4*3} = 35\sqrt[3]{12}[/tex]
33) [tex]\frac{6\sqrt[3]{-4} }{3\sqrt[3]{-2} } = 2*\sqrt[3]{\frac{-4}{-2} } = 2\sqrt[3]{2}[/tex]
34 ) 7 - [tex]\frac{5\sqrt{6} }{\sqrt{216} } = 7 - \frac{5\sqrt{6} }{6} = 7 - \frac{5}{6} \sqrt{6}[/tex]
35) 5[tex]\sqrt[3]{10} *2\sqrt[3]{-\frac{1}{2} } = 10*\sqrt[3]{10*(-\frac{1}{2}) } = 10\sqrt[3]{-5}[/tex]
36 ) [tex]\frac{\sqrt{0,1}: \sqrt{0,004} }{(-0,2)^2} = \frac{\sqrt{0,1 : 0,004} }{0,04} =[/tex] [tex]\frac{\sqrt{25} }{0,04} = \frac{5}{0,04} = 125[/tex]
Szczegółowe wyjaśnienie:
[tex]\sqrt{a*b} = \sqrt{a} *\sqrt{b}[/tex]
[tex]\sqrt{\frac{a}{b} } = \frac{\sqrt{a} }{\sqrt{b} }[/tex]
Korzystamy z własności pierwiastków:
[tex]\sqrt{a}=b \ \Leftrightarrow \ b^{2} = a\\\\(\sqrt{a})^{2} = a\\\\\sqrt[3]{b} = b \ \Leftrightarrow \ b^{3} = a\\\\(\sqrt[3]{a})^{3} = a\\\\\sqrt{a}\cdot\sqrt{b} = \sqrt{a\cdot b}\\\\\sqrt[3]{a}\cdot\sqrt[3]{b} = \sqrt[3]{a\cdot b}\\\\\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\\\\\frac{\sqrt[3]{a}}{\sqrt[3]{b}} = \sqrt[3]{\frac{a}{b}}[/tex]
[tex]26) \ \sqrt{25a^{4}} = \sqrt{25}\cdot\sqrt{a^{4}} = 5a^{2} \ \Leftrightarrow \ (5a^{2})^{2} =24a^{4}\\\\27) \ \sqrt{b^{18}} = b^{9}\\\\28) \ \sqrt[3]{216x^{9}y^{3}} = 6x^{3}y\\\\29) \ \sqrt{\frac{64x^{2}}{y^{10}}} = \frac{\sqrt{64x^{2}}}{\sqrt{y^{10}}}}=\frac{8x}{y^{5}}[/tex]
[tex]30) \ 2\sqrt{5}\cdot4\sqrt{3} = 2\cdot4\sqrt{5\cdot3} = 8\sqrt{15}\\\\31) \ \frac{5\sqrt{3}\cdot6\sqrt{2}}{10\sqrt{10}} = \frac{30\sqrt{6}}{10\sqrt{10}} = \frac{3\sqrt{6}}{\sqrt{10}}\cdot\frac{\sqrt{10}}{\sqrt{10}} = \frac{3\sqrt{60}}{10} = \frac{3\sqrt{4\cdot15}}{10} = \frac{3\cdot2\sqrt{15}}{10} = \frac{3\sqrt{15}}{5}[/tex]
[tex]32) \ 7\sqrt[3]{4}\cdot5\sqrt[3]{3} = 35\sqrt[3]{4\cdot3} = 35\sqrt[3]{12}\\\\33) \ \frac{6\sqrt[3]{-4}}{3\sqrt[3]{-2}} = 2\sqrt[3]{\frac{-4}{-2}} = 2\sqrt[3]{2}\\\\34) \ 7-\frac{5\sqrt{6}}{\sqrt{216}} = 7-\frac{5\sqrt{6}}{\sqrt{36\cdot6}}=7-\frac{5\sqrt{6}}{6\sqrt{6}} = 7-\frac{5}{6} = 6\frac{6}{6}-\frac{5}{6} = 6\frac{1}{6}[/tex]
[tex]35) \ 5\sqrt[3]{10}\cdot2\sqrt[3]{-\frac{1}{2}}=10\sqrt[3]{10\cdot(-\frac{1}{2})} = 10\sqrt[3]{-5}\\\\36) \ \frac{\sqrt{0,1}:\sqrt{0,004}}{(-0,2)^{2}} = \frac{\sqrt{100:4}}{0,04} =\frac{\sqrt{25}}{0,04} = \frac{5}{0,04} = \frac{500}{4} = 125[/tex]
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Odpowiedź:
26) [tex]\sqrt{25 a^4} = \sqrt{25} *\sqrt{a^4} = 5 a^2[/tex] bo ( 5 a²)² = 25 [tex]a^4[/tex]
27) [tex]\sqrt{b^{18}} = b^9[/tex] ([tex]b^9)^2 = b^{9*2} = b^{18}[/tex]
28 ) [tex]\sqrt[3]{216 x^9 y^3} = 6 x^3 y[/tex] ( 6 [tex]x^3 y)^3 = 6^3*(x^3)^3*y^3 = 216 x^9 y^3[/tex]
29) [tex]\sqrt{\frac{64x^2}{y^{10}} } = \frac{8x}{y^5}[/tex] ( [tex]\frac{8x}{y^5} )^2=\frac{64x^2}{y^{10}}[/tex]
30) 2[tex]\sqrt{5*4\sqrt{3} } = 8 \sqrt{5*3} = 8 \sqrt{15}[/tex]
31) [tex]\frac{5\sqrt{3}*6\sqrt{2} }{10\sqrt{10} } = \frac{5*2*3\sqrt{6} }{10\sqrt{10} } =\frac{3\sqrt{6} }{\sqrt{10} } = 3\sqrt{0,6}[/tex]
32 ) 7[tex]\sqrt[3]{4} *5\sqrt[3]{3} = 4=35\sqrt[3]{4*3} = 35\sqrt[3]{12}[/tex]
33) [tex]\frac{6\sqrt[3]{-4} }{3\sqrt[3]{-2} } = 2*\sqrt[3]{\frac{-4}{-2} } = 2\sqrt[3]{2}[/tex]
34 ) 7 - [tex]\frac{5\sqrt{6} }{\sqrt{216} } = 7 - \frac{5\sqrt{6} }{6} = 7 - \frac{5}{6} \sqrt{6}[/tex]
35) 5[tex]\sqrt[3]{10} *2\sqrt[3]{-\frac{1}{2} } = 10*\sqrt[3]{10*(-\frac{1}{2}) } = 10\sqrt[3]{-5}[/tex]
36 ) [tex]\frac{\sqrt{0,1}: \sqrt{0,004} }{(-0,2)^2} = \frac{\sqrt{0,1 : 0,004} }{0,04} =[/tex] [tex]\frac{\sqrt{25} }{0,04} = \frac{5}{0,04} = 125[/tex]
Szczegółowe wyjaśnienie:
[tex]\sqrt{a*b} = \sqrt{a} *\sqrt{b}[/tex]
[tex]\sqrt{\frac{a}{b} } = \frac{\sqrt{a} }{\sqrt{b} }[/tex]
Szczegółowe wyjaśnienie:
Pierwiastki
Korzystamy z własności pierwiastków:
[tex]\sqrt{a}=b \ \Leftrightarrow \ b^{2} = a\\\\(\sqrt{a})^{2} = a\\\\\sqrt[3]{b} = b \ \Leftrightarrow \ b^{3} = a\\\\(\sqrt[3]{a})^{3} = a\\\\\sqrt{a}\cdot\sqrt{b} = \sqrt{a\cdot b}\\\\\sqrt[3]{a}\cdot\sqrt[3]{b} = \sqrt[3]{a\cdot b}\\\\\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\\\\\frac{\sqrt[3]{a}}{\sqrt[3]{b}} = \sqrt[3]{\frac{a}{b}}[/tex]
[tex]26) \ \sqrt{25a^{4}} = \sqrt{25}\cdot\sqrt{a^{4}} = 5a^{2} \ \Leftrightarrow \ (5a^{2})^{2} =24a^{4}\\\\27) \ \sqrt{b^{18}} = b^{9}\\\\28) \ \sqrt[3]{216x^{9}y^{3}} = 6x^{3}y\\\\29) \ \sqrt{\frac{64x^{2}}{y^{10}}} = \frac{\sqrt{64x^{2}}}{\sqrt{y^{10}}}}=\frac{8x}{y^{5}}[/tex]
[tex]30) \ 2\sqrt{5}\cdot4\sqrt{3} = 2\cdot4\sqrt{5\cdot3} = 8\sqrt{15}\\\\31) \ \frac{5\sqrt{3}\cdot6\sqrt{2}}{10\sqrt{10}} = \frac{30\sqrt{6}}{10\sqrt{10}} = \frac{3\sqrt{6}}{\sqrt{10}}\cdot\frac{\sqrt{10}}{\sqrt{10}} = \frac{3\sqrt{60}}{10} = \frac{3\sqrt{4\cdot15}}{10} = \frac{3\cdot2\sqrt{15}}{10} = \frac{3\sqrt{15}}{5}[/tex]
[tex]32) \ 7\sqrt[3]{4}\cdot5\sqrt[3]{3} = 35\sqrt[3]{4\cdot3} = 35\sqrt[3]{12}\\\\33) \ \frac{6\sqrt[3]{-4}}{3\sqrt[3]{-2}} = 2\sqrt[3]{\frac{-4}{-2}} = 2\sqrt[3]{2}\\\\34) \ 7-\frac{5\sqrt{6}}{\sqrt{216}} = 7-\frac{5\sqrt{6}}{\sqrt{36\cdot6}}=7-\frac{5\sqrt{6}}{6\sqrt{6}} = 7-\frac{5}{6} = 6\frac{6}{6}-\frac{5}{6} = 6\frac{1}{6}[/tex]
[tex]35) \ 5\sqrt[3]{10}\cdot2\sqrt[3]{-\frac{1}{2}}=10\sqrt[3]{10\cdot(-\frac{1}{2})} = 10\sqrt[3]{-5}\\\\36) \ \frac{\sqrt{0,1}:\sqrt{0,004}}{(-0,2)^{2}} = \frac{\sqrt{100:4}}{0,04} =\frac{\sqrt{25}}{0,04} = \frac{5}{0,04} = \frac{500}{4} = 125[/tex]