(3pierwiastek z 2)^9 pierwiastek z 7 * 5 pierwiastek z 7 usuń niewymierność z mianownika : 3-2pierwiastek z 3 / 4pierwiastek z 3 oblicz : (7pierwiastek z 2-3 pierwiastek z 8) * pierwiastek z 2

[latex] (sqrt[3]{2} )[/latex]⁹ = ([latex] (sqrt[3]{2} )[/latex]³)³ = 2³ = 8 [latex] sqrt{7} [/latex] · 5 [latex] sqrt{7} [/latex] = 5 · 7 = 35 [latex] frac{3-2 sqrt{3} }{4 sqrt{3} } [/latex] = [latex] frac{(3-2 sqrt{3})4 sqrt{3} }{4 sqrt{3}* 4sqrt{3} } [/latex] = [latex] frac{12 sqrt{3}-8*3 }{16*3} [/latex] = [latex] frac{12( sqrt{3}-2) }{48} [/latex] = [latex] frac{ sqrt{3}-2 }{4} [/latex] (7[latex] sqrt{2} [/latex] - 3[latex] sqrt{8} [/latex]) [latex] sqrt{2} [/latex] = 7[latex] sqrt{4} [/latex] - 3[latex] sqrt{16} [/latex] = 7 · 2 - 3 · 4 = 14 - 12 = 2