Question

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Answer 1

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Answer 2

$6) \\ \\ a) \\ \\ \sqrt{10} \times \sqrt{7} = \sqrt{10 \times 7} = \sqrt{70}$

$b) \\ \\ \sqrt{11} \times ( - \sqrt{5}) = - \sqrt{11} \times \sqrt{5} = - \sqrt{11 \times 5} = - \sqrt{55}$

$c) \\ \\ \sqrt{2} \times \sqrt{3} \times \sqrt{6} = \sqrt{2 \times 3 \times 6} = \sqrt{36} = \sqrt{ {6}^{2} } = 6$

$d) \\ \\ ( - \sqrt{6}) \times \sqrt{ \frac{7}{2} } = - \sqrt{6} \times \sqrt{ \frac{7}{2} } = - \sqrt{6 \times \frac{7}{2} } = - \sqrt{3 \times 7} = - \sqrt{21}$

$e) \\ \\ \sqrt{18} \times ( - \sqrt{ \frac{1}{2} }) = - \sqrt{18} \times \sqrt{ \frac{1}{2} } = - \sqrt{18 \times \frac{1}{2} } = - \sqrt{9} = \sqrt{ {3}^{2} } = 3$

$f) \\ \\ \sqrt{ \frac{1}{2} } \times \sqrt{ \frac{2}{3} } \times \sqrt{ \frac{3}{4} } = \sqrt{ \frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} } = \sqrt{ \frac{1}{3} \times \frac{3}{4} } = \sqrt{ \frac{1}{4} } = \frac{ \sqrt{1} }{ \sqrt{4} } = \frac{1}{ \sqrt{ {2}^{2} } } = \frac{1}{2}$

$g) \\ \\ \sqrt{20} : \sqrt{5} = \sqrt{20 : 5} = \sqrt{4} = \sqrt{ {2}^{2} } = 2$

$h) \\ \\ \sqrt{98} : ( - \sqrt{2}) = - \sqrt{98} : \sqrt{2} = - \sqrt{98 : 2} = - \sqrt{49} = \sqrt{ {7}^{2} } = 7$

$i) \\ \\ \sqrt{3} \times \sqrt{8} : \sqrt{6} = \sqrt{3 \times 8 : 6} = \sqrt{4} = \sqrt{ {2}^{2} } = 2$

$7) \\ \\ a) \\ \\ 2 \sqrt{3} \times (3 \sqrt{5}) = 2 \sqrt{3} \times 3 \sqrt{5} = 6 \sqrt{3} \sqrt{5} = 6 \sqrt{3 \times 5} = 6 \sqrt{15}$

$b) \\ \\ ( - 3 \sqrt{7}) \times (2 \sqrt{2}) = - 3 \sqrt{7} \times 2 \sqrt{2} = - 6 \sqrt{7} \sqrt{2} = - 6 \sqrt{7 \times 2} = - 6 \sqrt{14}$

$c) \\ \\ 6 \sqrt{8} : ( - 3 \sqrt{2}) = - 6 \sqrt{8} : (3 \sqrt{2}) = - 2 \sqrt{4} = - 2 \times 2 = - 4$

$d) \\ \\ (30 \sqrt{12}) : ( - 2 \sqrt{2}) : ( - 5 \sqrt{3}) = (60 \sqrt{3}) : ( - 2 \sqrt{2}) : ( - 5 \sqrt{3}) = \frac{60 \sqrt{3} }{2 \sqrt{2} } \times \frac{1}{5 \sqrt{3} } = \frac{30}{ \sqrt{2} } \times \frac{1}{5} = \frac{6}{ \sqrt{2} } = \frac{6 \sqrt{2} }{ \sqrt{2} \sqrt{2} } = \frac{6 \sqrt{2} }{2} = 3 \sqrt{2}$

$e) \\ \\ ( - 3 \sqrt{5}) \times ( - \frac{ \sqrt{5} }{6}) = 3 \sqrt{5} \times \frac{ \sqrt{5} }{6} = \sqrt{5} \times \frac{ \sqrt{5} }{2} = \frac{ \sqrt{5} \sqrt{5} }{2} = \frac{5}{2}$

$f) \\ \\ \sqrt{ \frac{1}{3} } \times (2 \sqrt{1 \frac{1}{3} }) : ( - \sqrt{ \frac{64}{3} }) = \sqrt{ \frac{1}{3} } \times (2 \sqrt{ \frac{1}{3} }) : ( - \sqrt{ \frac{64}{3} }) = - \sqrt{ \frac{1}{3} } \times 2 \sqrt{ \frac{1}{3} } : \sqrt{ \frac{64}{3} } = - \frac{1}{3} \times 2 : nu \sqrt{ \frac{64}{3} } = - \frac{1}{3} \times \frac{2}{ \sqrt{ \frac{64}{3} } } = - \frac{1}{3} \times \frac{2}{ \frac{8}{ \sqrt{3} } } = - \frac{1}{3} \times \frac{ \sqrt{3} }{4} = - \frac{1 \sqrt{3} }{3 \times 4} = - \frac{ \sqrt{3} }{12}$