[tex]1.) \: \sqrt{75} = \sqrt{25} \times \sqrt{3} = 5 \sqrt{ 3} [/tex]
[tex]2.) \: \sqrt[3]{135} = \sqrt[3]{27} \times \sqrt[3]{5} = 3 \sqrt[3]{5} [/tex]
[tex]3.) \: \sqrt{12x^{3} } = \sqrt{4 \times 3 \times x^{2} \times x} = 2x \sqrt{3x} [/tex]
[tex]4.) \: \sqrt{150} = \sqrt{25} \times \sqrt{6} = 5 \sqrt{6} [/tex]
[tex]5.) \: \sqrt{28x^{4}y^{2} } = \sqrt{7 \times 4 \times x^{2} \times x^{2} \times {y}^{2} } = 2x^{2}y \sqrt{7} [/tex]
[tex]6.) \: \frac{ \sqrt{5} }{ \sqrt{6} } = \frac{ \sqrt{5} }{ \sqrt{6} } \times \frac{ \sqrt{6} }{ \sqrt{6} } = \frac{ \sqrt{5 \times 6} }{( \sqrt{6} )^{2} } = \frac{ \sqrt{30} }{6} [/tex]
[tex]7.) \: \frac{ \sqrt{24} }{ \sqrt{15} } = \frac{ \sqrt{24} }{ \sqrt{15} } \times \frac{ \sqrt{15} }{ \sqrt{15} } = \frac{ \sqrt{24 \times 15} }{( \sqrt{15})^{2} } = \frac{ \sqrt{3 \times 2 \times 4 \times 5 \times 3} }{15} = \frac{6 \sqrt{10} }{15} = \frac{2 \sqrt{10} }{5} [/tex]
[tex]8.) \: \frac{ \sqrt{20} }{ \sqrt{28} } = \frac{ \sqrt{20} }{ \sqrt{28} } \times \frac{ \sqrt{28} }{ \sqrt{28} } = \frac{ \sqrt{20 \times 28} }{( \sqrt{28})^{2} } = \frac{ \sqrt{5 \times 4 \times 7 \times 4} }{20} = \frac{4 \sqrt{35} }{20} = \frac{ \sqrt{35} }{5} [/tex]
[tex]9.) \: \frac{1}{ \sqrt{12} } = \frac{1}{ \sqrt{12} } \times \frac{ \sqrt{12} }{ \sqrt{12} } = \frac{ \sqrt{12} }{( \sqrt{12}) ^{2} } = \frac{ \sqrt{12} }{12} [/tex]
[tex]10.) \: \sqrt{ \frac{1}{3} } = \frac{ \sqrt{1} }{ \sqrt{3} } = \frac{ \sqrt{1} }{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } = \frac{ \sqrt{3 \times 1} }{( \sqrt{3})^{2} } = \frac{ \sqrt{3} }{3} [/tex]
