ajtatima la acest test dau coroanaaaa

5.

a) 3√7 - 2√7 + 8√7 - √7 = √7·(3 - 2 + 8 - 1) = 8√7

b) 2√(27) + 4√(12) - 3√(75) = 2√(3³) + 4√(2²·3) - 3√(5³) = 2·3√3 +4·2√3 -3·5√3 = 6√3 + 8√3 -15√3 = √3· (6 + 8 -15) = √3· (-1) = -√3

c) (5√5 + √45)·√5= (5√5 + √(5·3²)·√5=(5√5 + 3√(5)·√5 = 8√5·√5= 8 · 5 = 40

d)[tex](\sqrt{18} -\sqrt{6} ):\sqrt{2}=\frac{(\sqrt{18} -\sqrt{6} )}{\sqrt{2}}=\frac{(3\sqrt{2} -\sqrt{6} )}{\sqrt{2}}[/tex]

se rationalizeaza

[tex](\frac{3\sqrt{2}-\sqrt{6})\cdot\sqrt{2}}{2}=\frac{6-2\sqrt{3}}{2} =3-\sqrt{3}[/tex]

6.

a) [tex]\sqrt{(-7)^{2}} =7[/tex]

[tex]b)(\sqrt{3})^{5}\cdot (\sqrt{3}) =\\ \\ (\sqrt{3})^{5}=3^{2}\cdot\sqrt{3} \\ \\3^{2}\cdot\sqrt{3}\cdot \sqrt{3}=3^{2}\cdot3=3^{3}=\\ \\=27[/tex]

[tex]c)\sqrt{(75)^{3}}:(\sqrt{3})^{3}=\\ \\ 75=3\cdot5^{2} ;\sqrt{(75)^{3}}=75\cdot\sqrt{75} =75\cdot5\sqrt{3} =375\sqrt{3}\\ (\sqrt{3})^{3}=\sqrt{3}\cdot\sqrt{3}\cdot\sqrt{3} =3\sqrt{3}\\ \\375\sqrt{3}:3\sqrt{3}=125[/tex]

[tex]5) \\ \\ a) \\ \\ 3 \sqrt{7} - 2 \sqrt{7} + 8 \sqrt{7} - \sqrt{7} = 3 \sqrt{7} - 2 \sqrt{7} + 8 \sqrt{7} - 1 \sqrt{7} = (3 - 2 + 8 - 1) \sqrt{7} = 8 \sqrt{7} [/tex]

[tex]b) \\ \\ 2 \sqrt{27} + 4 \sqrt{12} - 3 \sqrt{75} = 6 \sqrt{3} + 8 \sqrt{3} - 15 \sqrt{3} = (6 + 8 - 15) \sqrt{3} = - 1 \sqrt{3} = - \sqrt{3} [/tex]

[tex]c) \\ \\ (5 \sqrt{5} + \sqrt{45}) \times \sqrt{5} = (5 \sqrt{5} + 3 \sqrt{5}) \sqrt{5} = 8 \sqrt{5} \sqrt{5} = 8 \times 5 = 40 [/tex]

[tex]d) \\ \\ ( \sqrt{18} - \sqrt{6}) : \sqrt{2} = (3 \sqrt{2} - \sqrt{6}) \div \sqrt{2} = \frac{3 \sqrt{2} - \sqrt{6} }{ \sqrt{2} } = \frac{(3 \sqrt{2} - \sqrt{6}) \sqrt{2} }{ \sqrt{2} \sqrt{2} } = \frac{(3 \sqrt{2} - \sqrt{6}) \sqrt{2} }{2} = \frac{6 - \sqrt{12} }{2} = \frac{6 - 2 \sqrt{3} }{2} = \frac{2(3 - \sqrt{3}) }{2} = 3 - \sqrt{3} [/tex]

[tex]6) \\ \\ a) \\ \\ \sqrt{ {( - 7)}^{2} } = | - 7| = 7 \\ \\ \sqrt{ {( - 7)}^{2} } = \sqrt{ {7}^{2} } = 7 [/tex]

[tex]b) \\ \\ {( \sqrt{3}) }^{5} \times \sqrt{3} = { \sqrt{3} }^{5} \times { \sqrt{3} }^{1} = { \sqrt{3} }^{5 + 1} = { \sqrt{3} }^{6} = {3}^{3} = 27 [/tex]

[tex]c) \\ \\ {( \sqrt{75}) }^{3} : {( \sqrt{3}) }^{3} = \frac{ { \sqrt{75} }^{3} }{ { \sqrt{3} }^{3}} = \frac{ {75}^{ \frac{3}{2} } }{ {3}^{ \frac{3}{2} } } = \frac{ {5}^{3} \times {3}^{ \frac{3}{2} } }{ {3}^{ \frac{3}{2} } } = {5}^{3} = 125 [/tex]

[tex]7) \\ \\ a = \sqrt{(5 \sqrt{2} - 7) ^{2} } - \sqrt{ {(2 - \sqrt{50}) }^{2} } \\ \\ a = 5 \sqrt{2} - 7 - \sqrt{ {(2 - 5 \sqrt{2}) }^{2} } \\ \\ a = 5 \sqrt{2} - 7 - (5 \sqrt{2} - 2) \\ \\ a = 5 \sqrt{2} - 7 - 5 \sqrt{2} + 2 \\ \\ a = - 7 + 2 \\ \\ a = - 5 [/tex]