Question

a doua parte ajutor

Answer 1

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Answer 2

${( \sqrt{5} + 1) }^{2} = { \sqrt{5} }^{2} + 2 \sqrt{5} \times 1 + {1}^{2} = 5 + 2 \sqrt{5} + 1 = 6 + 2 \sqrt{5}$

${(2 \sqrt{5} + 3 \sqrt{5}) }^{2} = 2 \sqrt{5} + 3 \sqrt{5} = (2 + 3) \sqrt{5} = 5 \sqrt{5} = {(5 \sqrt{5}) }^{2} = {5}^{2} \times { \sqrt{5} }^{2} = 25 \times 5 = 125$

${( \sqrt{3} - 2) }^{2} = { \sqrt{3} }^{2} - 2 \sqrt{3} \times 2 + {2}^{2} = 3 - 4 \sqrt{3} + 4 = 7 - 4 \sqrt{3}$

$\sqrt{3} + \sqrt{12} + \sqrt{27} + \sqrt{48} + \sqrt{75} + \sqrt{108} + \sqrt{147} = \sqrt{3} + 2 \sqrt{3} + 3 \sqrt{3} + 4 \sqrt{3} + 5 \sqrt{3} + 6 \sqrt{3} + 7 \sqrt{3} = 1 \sqrt{3} + 2 \sqrt{3} + 3 \sqrt{3} + 4 \sqrt{3} + 5 \sqrt{3} + 6 \sqrt{3} + 7 \sqrt{3} = (1 + 2 + 3 + 4 + 5 + 6 + 7) \sqrt{3} = 28 \sqrt{3}$