[tex]a)3 \sqrt{5} = \sqrt{ {3}^{2} \times 5} = \sqrt{9 \times 5} = \sqrt{45} [/tex]
[tex]b)7 \sqrt{6} = \sqrt{ {7}^{2} \times 6} = \sqrt{49 \times 6} = \sqrt{294} [/tex]
[tex]c) - 9 \sqrt{2} = \sqrt{( { - 9}^{2}) \times 2} = \sqrt{81 \times 2} = \sqrt{162} [/tex]
[tex]d) - \frac{1}{2} \sqrt{3} = \sqrt{ { (- \frac{1}{2}) }^{2} \times 3} = \sqrt{ \frac{1}{4} \times 3} = \sqrt{ \frac{3}{4} } [/tex]
[tex]e) \frac{3}{5} \sqrt{ \frac{1}{2} } = \sqrt{ ({ \frac{3}{5}) }^{2} \times \frac{1}{2} } = \sqrt{ \frac{9}{25} \times \frac{1}{2} } = \sqrt{ \frac{9}{50} } [/tex]
[tex]f) \frac{5}{7} \sqrt{3} = \sqrt{ {( \frac{5}{7}) }^{2} \times 3 } = \sqrt{ \frac{25}{49} \times 3} = \sqrt{ \frac{75}{49} } [/tex]
[tex]g) - \frac{2}{3} \sqrt{ \frac{3}{2} } = \sqrt{ {( - \frac{2}{3} )}^{2} \times \frac{3}{2} } = \sqrt{ \frac{4}{9} \times \frac{3}{2} } = \sqrt{ \frac{2}{3} } [/tex]
[tex]h)0.(3) \sqrt{15} = \frac{3}{10} \sqrt{15} = \sqrt{ { (\frac{3}{10}) }^{2} \times 15} = \sqrt{ \frac{9}{100} \times 15 } = \sqrt{ \frac{135}{100} } [/tex]
[tex]i) - 0.(1) \sqrt{2} = - \frac{1}{9} \sqrt{2} = \sqrt{ {( - \frac{1}{9} )}^{2} \times 2 } = \sqrt{ \frac{1}{81} \times 2 } = \sqrt{ \frac{2}{81} } [/tex]
