Question

Va rog ajutati-ma!Urgent va rog​

Answer 1

$\sqrt{ {2}^{7} } = {2}^{3} \sqrt{2} = 8 \sqrt{2} \\ \sqrt{ {3}^{11} } = \sqrt{ {3}^{10} \times 3 } = {3}^{5} \sqrt{3} \\ \sqrt{ {3}^{3} \times {5}^{5} \times {7}^{7} } = \sqrt{ {3}^{2} \times 3 \times {5}^{4} \times 5 \times {7}^{6} \times 7} = 3 \times {5}^{2} \times {7}^{3} \sqrt{3 \times 5 \times 7} \\ \sqrt{ {2}^{5} \times {3}^{7} } ={2}^{2} \times {3}^{3} \sqrt{2 \times 3} = 4 \times 27 \sqrt{6} = 108 \sqrt{6} \\ \sqrt{ {( - 2)}^{3} \times {( - 3)}^{3}} = \sqrt{ - 8 \times - 27} = \sqrt{216} = \sqrt{ {2}^{3} \times {3}^{3} } = 2 \times 3 \sqrt{2 \times 3} = 6 \sqrt{6} \\ \sqrt{2 \times {2}^{3} \times {2}^{5} \times {2}^{8} } = \sqrt{ {2}^{17} } = \sqrt{ {2}^{16} \times 2 } = {2}^{8} \sqrt{2} \\ \sqrt{ {2}^{2n + 1} } \: orice \: nr. \: inmultit \: cu \: 2 \: este \: par = > 2n \: este \: par = > 2n + 1 \: va \: deveni \: impar = > \sqrt{ {2}^{2n + 1} } = {2}^{n} \sqrt{2} \\ \sqrt{ {3}^{2n + 3} } = \sqrt{ {3}^{2n + 2 + 1} } \: \: \: \: \: \: \: 2n + 2 \: este \: par. \: iar \: 2n + 2 +1 \: este \: impar \: = > \sqrt{ {3}^{2n + 3} } = {3}^{n + 1} \sqrt{3}$