hej prosze o rozwiazanie i blagam o wytlumaczenie zadan z matmy z dzialu ,,dzialanie na pierwiastkach,, wszystko jest w zalaczniku i prosze o rozwiazanie zadan 13,14,15 i nie przyklad tylko rozwiazanie i wytlumaczenie :)
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1.



![\sqrt[3]{17^{3}} = \sqrt[3]{17^{3}} = \sqrt[3]{17*17*17} = 17 \sqrt[3]{17^{3}} = \sqrt[3]{17^{3}} = \sqrt[3]{17*17*17} = 17](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B17%5E%7B3%7D%7D+%3D+%5Csqrt%5B3%5D%7B17%5E%7B3%7D%7D+%3D+%5Csqrt%5B3%5D%7B17%2A17%2A17%7D+%3D+17)
![(\sqrt[3]{12})^{3} = (\sqrt[3]{12^{3}}) = (\sqrt[3]{12*12*12}) = 12 (\sqrt[3]{12})^{3} = (\sqrt[3]{12^{3}}) = (\sqrt[3]{12*12*12}) = 12](https://tex.z-dn.net/?f=%28%5Csqrt%5B3%5D%7B12%7D%29%5E%7B3%7D+%3D+%28%5Csqrt%5B3%5D%7B12%5E%7B3%7D%7D%29+%3D+%28%5Csqrt%5B3%5D%7B12%2A12%2A12%7D%29+%3D+12)
![(\sqrt[3]{11})^{6} = \sqrt[3]{11^{2} *11^{2}*11^{2}} = 11^{2} = 121 (\sqrt[3]{11})^{6} = \sqrt[3]{11^{2} *11^{2}*11^{2}} = 11^{2} = 121](https://tex.z-dn.net/?f=%28%5Csqrt%5B3%5D%7B11%7D%29%5E%7B6%7D+%3D+%5Csqrt%5B3%5D%7B11%5E%7B2%7D+%2A11%5E%7B2%7D%2A11%5E%7B2%7D%7D+%3D+11%5E%7B2%7D+%3D+121)
![\sqrt[3]{3^{9}} = \sqrt[3]{3^{3}*3^{3}*3^{3}} = 3^{3} = 27 \sqrt[3]{3^{9}} = \sqrt[3]{3^{3}*3^{3}*3^{3}} = 3^{3} = 27](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B3%5E%7B9%7D%7D+%3D+%5Csqrt%5B3%5D%7B3%5E%7B3%7D%2A3%5E%7B3%7D%2A3%5E%7B3%7D%7D+%3D+3%5E%7B3%7D+%3D+27)




zad. 2
Pole kwadratu:
a)
b)
c)
d)
zad 3
Objętość sześcianu = Pole podstawy * wysokość =
a) Objętość =![\sqrt[3]{2}*\sqrt[3]{2}*\sqrt[3]{2} = \sqrt[3]{2*2*2} = 2m^{3} \sqrt[3]{2}*\sqrt[3]{2}*\sqrt[3]{2} = \sqrt[3]{2*2*2} = 2m^{3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2%7D%2A%5Csqrt%5B3%5D%7B2%7D%2A%5Csqrt%5B3%5D%7B2%7D+%3D+%5Csqrt%5B3%5D%7B2%2A2%2A2%7D+%3D+2m%5E%7B3%7D)
b) Objętość =![2\sqrt[3]{3} * 2\sqrt[3]{3} * 2\sqrt[3]{3} = \sqrt[3]{2^{3}*3*2^{3}*3*2^{3}*3}=2^{3}*3 = 24dm^{3} 2\sqrt[3]{3} * 2\sqrt[3]{3} * 2\sqrt[3]{3} = \sqrt[3]{2^{3}*3*2^{3}*3*2^{3}*3}=2^{3}*3 = 24dm^{3}](https://tex.z-dn.net/?f=2%5Csqrt%5B3%5D%7B3%7D+%2A+2%5Csqrt%5B3%5D%7B3%7D+%2A+2%5Csqrt%5B3%5D%7B3%7D+%3D+%5Csqrt%5B3%5D%7B2%5E%7B3%7D%2A3%2A2%5E%7B3%7D%2A3%2A2%5E%7B3%7D%2A3%7D%3D2%5E%7B3%7D%2A3+%3D+24dm%5E%7B3%7D)
c) Objętość =![5\sqrt[3]{9} * 5\sqrt[3]{9} * 5\sqrt[3]{9} = \sqrt[3]{5^{3}*9*5^{3}*9*5^{3}*9}=5^{3}*9 = 1125cm^{3} 5\sqrt[3]{9} * 5\sqrt[3]{9} * 5\sqrt[3]{9} = \sqrt[3]{5^{3}*9*5^{3}*9*5^{3}*9}=5^{3}*9 = 1125cm^{3}](https://tex.z-dn.net/?f=5%5Csqrt%5B3%5D%7B9%7D+%2A+5%5Csqrt%5B3%5D%7B9%7D+%2A+5%5Csqrt%5B3%5D%7B9%7D+%3D+%5Csqrt%5B3%5D%7B5%5E%7B3%7D%2A9%2A5%5E%7B3%7D%2A9%2A5%5E%7B3%7D%2A9%7D%3D5%5E%7B3%7D%2A9+%3D+1125cm%5E%7B3%7D)
d) Objętość =![3\sqrt[3]{12} * 3\sqrt[3]{12} * 3\sqrt[3]{12} = \sqrt[3]{3^{3}*12*3^{3}*12*3^{3}*12}=3^{3}*12 = 324mm^{3} 3\sqrt[3]{12} * 3\sqrt[3]{12} * 3\sqrt[3]{12} = \sqrt[3]{3^{3}*12*3^{3}*12*3^{3}*12}=3^{3}*12 = 324mm^{3}](https://tex.z-dn.net/?f=3%5Csqrt%5B3%5D%7B12%7D+%2A+3%5Csqrt%5B3%5D%7B12%7D+%2A+3%5Csqrt%5B3%5D%7B12%7D+%3D+%5Csqrt%5B3%5D%7B3%5E%7B3%7D%2A12%2A3%5E%7B3%7D%2A12%2A3%5E%7B3%7D%2A12%7D%3D3%5E%7B3%7D%2A12+%3D+324mm%5E%7B3%7D)