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5)
![(19 \sqrt{ \frac{13}{19} } - 13\sqrt{\frac{19}{13}})^2 = (\sqrt{\frac{19^2*13}{19}} - \sqrt{\frac{13^2*19}{13}})^2 = (0)^2 = 0 (19 \sqrt{ \frac{13}{19} } - 13\sqrt{\frac{19}{13}})^2 = (\sqrt{\frac{19^2*13}{19}} - \sqrt{\frac{13^2*19}{13}})^2 = (0)^2 = 0](https://tex.z-dn.net/?f=%2819+%5Csqrt%7B+%5Cfrac%7B13%7D%7B19%7D+%7D+-+13%5Csqrt%7B%5Cfrac%7B19%7D%7B13%7D%7D%29%5E2+%3D+%28%5Csqrt%7B%5Cfrac%7B19%5E2%2A13%7D%7B19%7D%7D+-+%5Csqrt%7B%5Cfrac%7B13%5E2%2A19%7D%7B13%7D%7D%29%5E2+%3D+%280%29%5E2+%3D+0)
6)![\sqrt[3]{\sqrt{43} + 4} * \sqrt[3]{\sqrt{43} - 4} = \sqrt[3]{(\sqrt{43} + 4)(\sqrt{43} - 4)}= \sqrt[3]{\sqrt{43} + 4} * \sqrt[3]{\sqrt{43} - 4} = \sqrt[3]{(\sqrt{43} + 4)(\sqrt{43} - 4)}=](https://tex.z-dn.net/?f=+%5Csqrt%5B3%5D%7B%5Csqrt%7B43%7D+%2B+4%7D+%2A+%5Csqrt%5B3%5D%7B%5Csqrt%7B43%7D+-+4%7D+%3D+%5Csqrt%5B3%5D%7B%28%5Csqrt%7B43%7D+%2B+4%29%28%5Csqrt%7B43%7D+-+4%29%7D%3D)
6)
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