Explicație pas cu pas:
2.
[tex]a = \frac{2 \sqrt{10} }{ \sqrt{5} } - \frac{5 \sqrt{10} }{ \sqrt{2} } + 5 \sqrt{5} = 2 \sqrt{2} - 5 \sqrt{5} + 5 \sqrt{5} = 2 \sqrt{2}\\[/tex]
[tex]b = \frac{2 \sqrt{10} }{ \sqrt{5} } - \frac{5 \sqrt{10} }{ \sqrt{2} } - 2 \sqrt{2} = 2 \sqrt{2} - 5 \sqrt{5} - 2 \sqrt{2} = - 5\sqrt{5}\\[/tex]
[tex]5 \sqrt{5}a + 2 \sqrt{2}b = 5 \sqrt{5}(2 \sqrt{2}) + 2 \sqrt{2}( - 5 \sqrt{5} ) = 10 \sqrt{10} - 10 \sqrt{10} = \bf 0\\[/tex]
3.
[tex]a = 22 \sqrt{7} - 18 \sqrt{2} + 18 \sqrt{2} - 9 \sqrt{7} = 13 \sqrt{7} \\[/tex]
[tex]b = 20 \sqrt{2} - 20 \sqrt{2} + 50 \sqrt{5} - 50 \sqrt{5} = 0\\[/tex]
[tex]a \cdot b = 13 \sqrt{7} \cdot 0 = \bf 0\\[/tex]
[tex] {a}^{b} = ({13 \sqrt{7} })^{0} = \bf 1\\[/tex]
4.
[tex]a = \sqrt{100 + (2 + 4 + 6 + ... + 198)} = \sqrt{100 + 2(1 + 2 + 3 + ... + 99)} = \sqrt{100 + 2 \cdot \frac{99 \cdot 100}{2} } = \sqrt{100 + 99 \cdot 100} = \sqrt{100 \cdot (1 + 99)} = \sqrt{100 \cdot 100} = \sqrt{ {100}^{2} } = 100 = \bf {10}^{2} [/tex]
