1.
[tex] \sqrt{ {3}^{2} } = 3[/tex]
[tex] \sqrt{ {3}^{2} \times 5} = 3 \sqrt{5} [/tex]
[tex] \sqrt{ {5}^{3} } = \sqrt{ {5}^{2} \times 5} = 5 \sqrt{5} [/tex]
[tex] \sqrt{12} = \sqrt{4 \times 3} = \sqrt{ {2}^{2} \times 3} = 2 \sqrt{3} [/tex]
[tex] \sqrt{24} = \sqrt{4 \times 6} = \sqrt{ {2}^{2} \times 6} = 2 \sqrt{6} [/tex]
[tex] \sqrt{27} = \sqrt{ {3}^{3} } = \sqrt{ {3}^{2} \times 3} = 3 \sqrt{3} [/tex]
2.
[tex]2 \sqrt{3} = \sqrt{ {2}^{2} \times 3} = \sqrt{4 \times 3} = \sqrt{12} [/tex]
[tex]3 \sqrt{5} = \sqrt{ {3}^{2} \times 5} = \sqrt{9 \times 5} = \sqrt{45} [/tex]
[tex] - 5 \sqrt{2} = - \sqrt{ {5}^{2} \times 2} = - \sqrt{25 \times 2} = - \sqrt{50} [/tex]
[tex]2 \sqrt{2} = \sqrt{ {2}^{2} \times 2} = \sqrt{ {2}^{3} } = \sqrt{8} [/tex]
[tex]3 \sqrt{3} = \sqrt{ {3}^{2} \times 3} = \sqrt{ {3}^{3} } = \sqrt{27} [/tex]
[tex]6 \sqrt{11} = \sqrt{ {6}^{2} \times 11} = \sqrt{36 \times 11} = \sqrt{396} [/tex]
[tex] - 4 \sqrt{6} = - \sqrt{ {4}^{2} \times 6} = - \sqrt{16 \times 6} = - \sqrt{96} [/tex]
