Odpowiedź:
zad.1
[tex]a) \: \sqrt{16 \times 9} = \sqrt{16} \times \sqrt{9} = 4 \times 3 = 12 \\ b) \: \sqrt{100 \times 64} = \sqrt{100} \times \sqrt{64} = 10 \times 8 = 80 \\ c) \: \sqrt{ {6}^{2} \times {5}^{2} } = \sqrt{ {6}^{2} } \times \sqrt{ {5}^{2} } = 6 \times 5 = 30 \\ d) \: \sqrt{4 \times 81 \times 9} = \sqrt{4} \times \sqrt{81} \times \sqrt{9} = 2 \times 9 \times 3 = 54 \\ [/tex]
[tex]e) \: \sqrt{16 \times 25 \times 49} = \sqrt{16} \times \sqrt{25} \times \sqrt{49} = 4 \times 5 \times 7 = 140 \\ f) \: \sqrt{ { {11}^{2} \times {2}^{2} } \times {3}^{2} } = \sqrt{ {11}^{2} } \times \times \sqrt{ {2}^{2} } \times \sqrt{ {3}^{2} } = 11 \times 2 \times 3 = 66 \\ [/tex]
[tex]g) \: \sqrt[3]{27 \times 64} = \sqrt[3]{27} \times \sqrt[3]{64} = 3 \times 4 = 12 \\ h) \: \sqrt[3]{8 \times 64} = \sqrt[3]{8} \times \sqrt[3]{64} = 2 \times 4 = 8 \\ i) \: \sqrt[3]{ {7}^{3} \times {9}^{3} } = \sqrt[3]{ {7}^{3} } \times \sqrt[3]{ {9}^{3} } = 7 \times 9 = 63 \\ [/tex]
[tex]j) \: \sqrt[3]{27 \times 64 \times 125} = \sqrt[3]{27} \times \sqrt[3]{64} \times \sqrt[3]{125} = 3 \times 4 \times 5 = 60 \\ k) \: \sqrt[3]{ {3}^{6} \times {5}^{3} \times {2}^{9} } = \sqrt[3]{ {3}^{6} } \times \sqrt[3]{ {5}^{3} } \times \sqrt[3]{ {2}^{9} } = {3}^{2} \times 5 \times {2}^{3} = 9 \times 5 \times 8 = 360 \\ l) \: \sqrt[3]{ {4}^{9} \times {6}^{3} \times 27 } = \sqrt[3]{ {4}^{9} } \times \sqrt[3]{ {6}^{3} \times \sqrt[3]{27} } = {4}^{3} \times 6 \times 3 = 64 \times 18 = 1152[/tex]
zad.2
[tex]a) \: \sqrt{1089} = \sqrt{ {3}^{2} \times {11}^{2} } = 3 \times 11 = 33 \\ b) \: \sqrt{676} = \sqrt{ {3}^{2} \times {13}^{2} } = 3 \times 13 = 39 \\ c) \: \sqrt{1764} = \sqrt{ {2}^{2} \times {3}^{2} \times {7}^{2} } = 2 \times 3 \times 7 = 42 \\ d) \: \sqrt{4356} = \sqrt{ {2}^{2} \times {3}^{2} \times {11}^{2} } 2 \times 3 \times 11 = 66 \\ e) \: \sqrt{7056} = \sqrt{ {2}^{4} \times {3}^{2} \times {11}^{2} } = {2}^{2} \times 3 \times 11 = 132 \\ f) \: \sqrt{19600} = \sqrt{ {2}^{4} \times {5}^{2} \times {7}^{2} } = {2}^{2} \times 5 \times 7 = 140[/tex]
