Explicație pas cu pas:
[tex]a) m_{g} = \sqrt{a \times b} = \sqrt{4 \sqrt{5} \times 10 \sqrt{5} } = \sqrt{4 \times 10 \sqrt{5 \times 5} } = \sqrt{4 \times 10 \sqrt{25} } = \sqrt{4 \times 10 \times \sqrt{ {5}^{2} } } = \sqrt{4 \times 10 \times 5} = \sqrt{40 \times 5} = \sqrt{200} = 10 \sqrt{2} [/tex]
[tex]b) m_{g} = \sqrt{a \times b} = \sqrt{9 \sqrt{7} \times 21 \sqrt{7} } = \sqrt{9 \times 21 \sqrt{7 \times 7} } = \sqrt{9 \times 21 \sqrt{49} } = \sqrt{9 \times 21 \times \sqrt{ {7}^{2} } } = \sqrt{9 \times 21 \times 7} = \sqrt{189 \times 7} = \sqrt{1323} = 21 \sqrt{3} [/tex]
[tex]c) m_{g} = \sqrt{a \times b} = \sqrt{32 \sqrt{5} \times 5 \sqrt{5} } = \sqrt{32 \times 5 \sqrt{5 \times 5} } = \sqrt{32 \times 5 \sqrt{25} } = \sqrt{32 \times 5 \times \sqrt{ {5}^{2} } } = \sqrt{32 \times 5 \times 5} = \sqrt{160 \times 5} = \sqrt{800} = 20 \sqrt{2} [/tex]
[tex]d) m_{g} = \sqrt{a \times b} = \sqrt{24 \sqrt{6} \times 7 \sqrt{6} } = \sqrt{24 \times 7 \sqrt{6 \times 6} } = \sqrt{24 \times 7 \sqrt{36} } = \sqrt{24 \times 7 \times \sqrt{ {6}^{2} } } = \sqrt{24 \times 7 \times 6} = \sqrt{168 \times 6} = \sqrt{1008} = 12 \sqrt{7} [/tex]
