Răspuns:
1
Explicație pas cu pas:
1 a.
[tex] \sqrt{121} = \sqrt{ {11}^{2} } = 11[/tex]
b.
[tex] \sqrt{225} = \sqrt{ {15}^{2} } = 15[/tex]
c.
[tex] \sqrt{961} = \sqrt{ {31}^{2} } = 31[/tex]
D.
[tex] \sqrt{9 \times 16} = \sqrt{ {3}^{2} \times {2}^{4} } = 3 \times {2}^{2} = 3 \times 4 = 12[/tex]
e.
[tex] \sqrt{25 \times 81} = \sqrt{ {5}^{2} \times {9}^{2} } = 5 \times 9 = 45[/tex]
f.
[tex] \sqrt{144 \times 361} = \sqrt{ {12}^{2} \times {19}^{2} } = 12 \times 19 = 228[/tex]
3.a.
[tex]2 \times \sqrt{5} = \sqrt{ {2}^{2} \times 5 } = \sqrt{20} [/tex]
b.
[tex] - 2 \times \sqrt[3]{2} = - \sqrt[3]{ {2}^{3} \times 2} = \sqrt[3]{16} [/tex]
c.
[tex]3 \times \sqrt{3} = \sqrt{ {3}^{2} \times 3 } = \sqrt{27} [/tex]
D.
[tex] - 3 \sqrt{3} = - \sqrt{27} [/tex]
e.
[tex]3 \times \sqrt[3]{3} = \sqrt[3]{ {3}^{3} \times 3} = \sqrt[3]{81} [/tex]
f.
[tex]5 \times \sqrt[3]{2} = \sqrt[3]{ {5}^{3} \times 2 } = \sqrt[3]{250} [/tex]
2.a.
[tex] \frac{2}{ \sqrt{6} } = \frac{2 \times \sqrt{6} }{ \sqrt{6} \times \sqrt{6} } = \frac{2 \sqrt{6} }{ \sqrt{ {6}^{2} } } = \frac{2 \sqrt{6} }{6} = \frac{ \sqrt{6} }{3} [/tex]
b.
[tex] \frac{1}{ \sqrt[3]{2} } = \frac{ \sqrt[3]{ {2}^{2} } }{ \sqrt[3]{2} \times \sqrt[3]{ {2}^{2} } } = \frac{ \sqrt[3]{ {2}^{2} } }{ \sqrt[3]{ {2}^{3} } } = \frac{ \sqrt[3]{ {2}^{2} } }{2} [/tex]
c.
[tex] \frac{1}{ \sqrt{3} - \sqrt{2} } = \frac{ \sqrt{3} + \sqrt{2} }{( \sqrt{3} - \sqrt{2)} \times ( \sqrt{3} + \sqrt{2)} } = \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{ {3}^{2} } - \sqrt{ {2}^{2} } } = \frac{ \sqrt{3} + \sqrt{2} }{3 - 2} = \sqrt{3} + \sqrt{2} [/tex]
D.
[tex] \frac{2}{ \sqrt{5} + \sqrt{3} } = \frac{2 \times ( \sqrt{5} - \sqrt{3}) }{5 - 3} = [/tex]
