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Решение на фото...........

Покрокове пояснення:

5.

a) [tex]\sqrt{64} +\sqrt{1000} = 8+10 = 18[/tex]

b) [tex]\sqrt[3]{7^{2}+15 }= \sqrt[3]{69}=4[/tex]

c) [tex]\sqrt{13^{2}} +\sqrt[3]{7^{3} } = 13 + 7 = 20[/tex]

d) [tex]\sqrt{2} *\sqrt{18} +3*\sqrt[3]{3} *\sqrt[3]{9} = \sqrt{36} + 3\sqrt[3]{27} = 6+9 = 15[/tex]

e) [tex]\frac{\sqrt{75}+2\sqrt{3} }{\sqrt{3} } = \frac{5\sqrt{3}+2\sqrt{3} }{\sqrt{3} } = \frac{7\sqrt{3}}{\sqrt{3}} =7[/tex]

6.

[tex]\frac{2}{5\sqrt{3} } = \frac{2}{5\sqrt{3} } * \frac{\sqrt{3} }{\sqrt{3} } = \frac{2\sqrt{3} }{5*3} =\frac{2\sqrt{3} }{15}[/tex]

7.

[tex]\frac{3\sqrt{6}+2}{2\sqrt{2} } = \frac{3\sqrt{6}+2}{2\sqrt{2} } * \frac{\sqrt{2} }{\sqrt{2}}=\frac{3\sqrt{12} +2\sqrt{2} }{4} = \frac{6\sqrt{3}+2\sqrt{2} }{4} = \frac{2(3\sqrt{3} + \sqrt{2} )}{4} = \frac{3\sqrt{3} + \sqrt{2} }{2}[/tex]

8.

a) [tex]\frac{15}{\sqrt{3} } = \frac{15}{\sqrt{3} } *\frac{\sqrt{3} }{\sqrt{3}} = \frac{15\sqrt{3} }{3}=5\sqrt{3}[/tex]

b) [tex]\frac{-3\sqrt{12} }{2\sqrt{6} } = \frac{-6\sqrt{3} }{2\sqrt{6} } = \frac{-3}{\sqrt{2} } = \frac{-3\sqrt{2} }{2}[/tex]

9.

[tex]\frac{2\sqrt{48}-2\sqrt{12} }{4\sqrt{3} } = \frac{8\sqrt{3}-4\sqrt{3} }{4\sqrt{3} } =\frac{4\sqrt{3} }{4\sqrt{3}} =1[/tex]