Răspuns:
Subiectul 1
1.
[tex]3 \sqrt{5} + 2 \sqrt{5} = 5 \sqrt{5} [/tex]
2.
[tex]5 \sqrt{2} = \sqrt{ {5}^{2} \times 2 } = \sqrt{25 \times 2} = \sqrt{50} [/tex]
3.
[tex]2 \sqrt{3} = \sqrt{2 {}^{2} \times 3} = \sqrt{4 \times 3} = \sqrt{12} \\ 7 \sqrt{2} = \sqrt{7 {}^{2} \times 2} = \sqrt{49 \times 2} = \sqrt{98} \\ 2 \sqrt{3} < \sqrt{98} [/tex]
4.
[tex] \frac{2 \sqrt{3} }{3} = \frac{6}{ \times } \\ 2 \sqrt{3} \times = 6 \times 3 \\ 2 \sqrt{3} \times = 18 \\ \times = \frac{18}{2 \sqrt{3} } \\ \times = \frac{18 \sqrt{3} }{6} \\ \times = 3 \sqrt{3} [/tex]
5.
[tex]2 \sqrt{7} \times 3 \sqrt{5} \\ = 2 \times 3 \times \sqrt{7} \times \sqrt{5} \\ = 6 \times \sqrt{35} \\ = 6 \sqrt{35} [/tex]
Subiectul 2
1.
[tex] \frac{15}{ \sqrt{45} } = \frac{15}{3 \sqrt{5} } = \frac{15 \sqrt{5} }{15} = \sqrt{5} [/tex]
2.
[tex]mg = \sqrt{3 \times 12} \\ = \sqrt{36} \\ = 6[/tex]
3.
[tex] \sqrt{2} - \sqrt{5} = \frac{1}{ \sqrt{2} + \sqrt{5} } [/tex]
4.
[tex]3 \sqrt{12} + \sqrt{27} \\ = 3 \times 2 \sqrt{3} + 3 \sqrt{3} \\ = 6 \sqrt{3} + 3 \sqrt{3} \\ = 9 \sqrt{3} [/tex]
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