Answer:
6.Ans;
[tex] \sqrt{18} = \sqrt{9} \sqrt{2} = 3 \sqrt{2} [/tex]
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[tex] - \sqrt{48} = - \sqrt{8} \sqrt{6} = - \sqrt{4} \sqrt{2} \sqrt{2} \sqrt{3} = - 2 \sqrt{4} \sqrt{3} = - 2 \times 2 \sqrt{3} = - 4 \sqrt{3} [/tex]
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[tex] \sqrt{75} = \sqrt{15} \sqrt{5} = \sqrt{5} \sqrt{3} \sqrt{5} = 5 \sqrt{3} [/tex]
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[tex] \sqrt{ \frac{30}{49} } = \frac{ \sqrt{30} }{ \sqrt{49} } = \frac{ \sqrt{5} \sqrt{6} }{ \sqrt{7} \sqrt{7} } = \frac{ \sqrt{5} \sqrt{6} }{7} = \frac{ \sqrt{30} }{7} [/tex]
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[tex] \sqrt{ \frac{10}{121} } = \frac{ \sqrt{10} }{ \sqrt{121} } = \frac{ \sqrt{5} \sqrt{2} }{ \sqrt{11} \sqrt{11} } = \frac{ \sqrt{10} }{11} [/tex]
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[tex] \sqrt[3]{40} = \sqrt[3]{8} \sqrt[3]{5} = 2 \sqrt[3]{5} [/tex]
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[tex] \sqrt[3]{54} = \sqrt[3]{27} \sqrt[3]{2} = 3 \sqrt[3]{2} [/tex]
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[tex] - \sqrt[3]{128} = - \sqrt[3]{64} \sqrt[3]{2} = - 4 \sqrt[3]{2} [/tex]
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[tex] \sqrt[3]{192} = \sqrt[3]{64} \sqrt[3]{3} = 4 \sqrt[3]{3} [/tex]
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[tex] \sqrt[3]{ \frac{3m}{8 {n}^{3} } } = \frac{ \sqrt[3]{3m} }{ \sqrt[3]{8 {n}^{3} } } = \frac{ \sqrt[3]{3m} }{2n} [/tex]
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[tex] \sqrt[3]{16 {a}^{5} } = \sqrt[3]{8 {a}^{3} } \sqrt[3]{2 {a}^{2} } = 2a \sqrt[3]{2 {a}^{2} } [/tex]
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[tex] \sqrt[4]{80} = \sqrt[4]{16} \sqrt[4]{5} = 2 \sqrt[4]{5} [/tex]
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[tex] \sqrt[4]{ \frac{32}{256} } = \frac{ \sqrt[4]{32} }{ \sqrt[4]{256} } = \frac{ \sqrt[4]{16} \sqrt[4]{2} }{ \sqrt[4]{16} \sqrt[4]{16} } = \frac{ \sqrt[4]{2} }{ \sqrt[4]{16} } = \frac{ \sqrt[3]{2} }{2} [/tex]
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[tex] \sqrt[4]{ \frac{4 {x}^{2} }{81 {y}^{4} } } = \frac{ \sqrt[4]{4 {x}^{2} } }{ \sqrt[4]{81 {y}^{4} } } = \frac{ \sqrt{2x} }{3y} [/tex]
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[tex] - \sqrt[5]{ \frac{3}{243} } = - \frac{ \sqrt[5]{3} }{ \sqrt[5]{243} } = - \frac{ \sqrt[5]{3} }{3} [/tex]
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[tex] \sqrt[5]{ \frac{375}{32 {x}^{6} } } = \frac{ \sqrt[5]{375} }{ \sqrt[5]{32 {x}^{6} } } = \frac{ \sqrt[5]{375 {x}^{4} } }{2 {x}^{2} } [/tex]
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7.Ans ;
[tex] \sqrt{36 {a}^{2} {b}^{3} } = 6ab \sqrt{b} [/tex]
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[tex] \sqrt{27 {a}^{4} {b}^{3} } = 3 {a}^{2} b \sqrt{3b} [/tex]
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[tex] \sqrt{72 {x}^{5} {y}^{2} } = 6 {x}^{2}y \sqrt{2x} [/tex]
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[tex] - \sqrt{ {112}^{3} {b}^{4} } = - 448 {b}^{2} \sqrt{7} [/tex]
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[tex] \sqrt{80 {m}^{4} {n}^{3} } = 4 {m}^{2}n \sqrt{5n} [/tex]
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[tex] \sqrt{64 {x}^{2} {y}^{3} } = 8xy \sqrt{y} [/tex]
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[tex] \sqrt[3]{16 {m}^{3} {n}^{3} } = 2mn \sqrt[3]{2} [/tex]
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[tex] \sqrt[3]{ - 54 {x}^{4} {b}^{3} } = - 3xb \sqrt[3]{2x} [/tex]
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[tex] - \sqrt[3]{128 {a}^{5} {y}^{3} } = - 4ay \sqrt[3]{2 {a}^{2} } [/tex]
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[tex] \sqrt[3]{24 {p}^{3} {q}^{5} } = 2pq \sqrt[3]{3 {q}^{2} } [/tex]
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[tex] \sqrt[4]{81 {x}^{4} {y}^{2} } = 3x \sqrt{y} [/tex]
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[tex] - \sqrt[4]{256 {a}^{4} {b}^{5} } = - 4ab \sqrt[4]{b} [/tex]
I hope I helped you^_^
