Răspuns:
a)
[tex] \sqrt{32} = \sqrt{ {2}^{5} } = 4 \sqrt{2} [/tex]
[tex] \sqrt{50} = \sqrt{2 \times {5}^{2} } = 5 \sqrt{2} [/tex]
[tex] \sqrt{8} = \sqrt{ {2}^{3} } = 2 \sqrt{2} [/tex]
[tex] \sqrt{98} = \sqrt{2 \times {7}^{2} } = 7 \sqrt{2} [/tex]
[tex] \sqrt{242} = \sqrt{2 \times {11}^{2} } = 11 \sqrt{2} [/tex]
[tex]4 \sqrt{2} - 5 \sqrt{2} + 2 \sqrt{2} - 7 \sqrt{2} + 11 \sqrt{2} = 5 \sqrt{2} [/tex]
b)
[tex] - \sqrt{162} = - \sqrt{2 \times {3}^{4} } = - 9 \sqrt{2} [/tex]
[tex] \sqrt{200} = \sqrt{2 \times {10}^{2} } = 10 \sqrt{2} [/tex]
[tex] \sqrt{72} = \sqrt{ {2}^{3} \times {3}^{2}} = 6 \sqrt{2} [/tex]
[tex] \sqrt{128} = \sqrt{ {2}^{7} } = 8 \sqrt{2} [/tex]
[tex] \sqrt{18} = \sqrt{2 \times {3}^{2} } = 3 \sqrt{2} [/tex]
[tex] - 9 \sqrt{2} + 10 \sqrt{2} - 6\sqrt{2} - 8 \sqrt{2} + 3 \sqrt{2} = - 10 \sqrt{2} [/tex]
c)
[tex] \sqrt{48} = \sqrt{ {2}^{4} \times 3 } = 4 \sqrt{3} [/tex]
[tex] \sqrt{75} = \sqrt{3 \times {5}^{2} } = 5 \sqrt{3} [/tex]
[tex] \sqrt{12} = \sqrt{ {2}^{2} \times 3 } = 2 \sqrt{3} [/tex]
[tex] \sqrt{243} = \sqrt{ {3}^{5} } = 9 \sqrt{3} [/tex]
[tex] \sqrt{147} = \sqrt{3 \times {7}^{2} } = 7 \sqrt{3} [/tex]
[tex]4 \sqrt{3} - 5 \sqrt{3} + 2 \sqrt{3} +9 \sqrt{3} - 7 \sqrt{3} = 3 \sqrt{3} [/tex]
d)
[tex] \sqrt{300} = \sqrt{3 \times {10}^{2} } = 10 \sqrt{3} [/tex]
[tex] \sqrt{192} = \sqrt{ {2}^{6} \times 3 } = 8 \sqrt{3} [/tex]
[tex] \sqrt{108} = \sqrt{ {2}^{2} \times {3}^{3} } = 6 \sqrt{3} [/tex]
[tex] \sqrt{27} = \sqrt{ {3}^{3} } = 3 \sqrt{3} [/tex]
[tex] \sqrt{432} = \sqrt{3 \times {12}^{2} } = 12 \sqrt{3} [/tex]
[tex]10 \sqrt{3} - 8 \sqrt{3} - 6 \sqrt{3} + 3 \sqrt{3} - 12 \sqrt{3} = - 13 \sqrt{3} [/tex]
