Usuń niewymierność z mianownika :
a) 4/3 pierwiastek z 6
b) pierwastek z 5 / 5 pierwiastek z 2
c) 1 / 5+ pierwiastek z 3
d) 2 / 2 pierwiastek z 2 - 1
Prosze o szybkie rozwiązanie i dokładne !! :) :)
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a)![\frac{4}{3\sqrt{6}}*\frac{\sqrt{6}}{\sqrt{6}}=\frac{4\sqrt{6}}{3*6}=\frac{4\sqrt{6}}{18}=\frac{2\sqrt{6}}{9} \frac{4}{3\sqrt{6}}*\frac{\sqrt{6}}{\sqrt{6}}=\frac{4\sqrt{6}}{3*6}=\frac{4\sqrt{6}}{18}=\frac{2\sqrt{6}}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%5Csqrt%7B6%7D%7D%2A%5Cfrac%7B%5Csqrt%7B6%7D%7D%7B%5Csqrt%7B6%7D%7D%3D%5Cfrac%7B4%5Csqrt%7B6%7D%7D%7B3%2A6%7D%3D%5Cfrac%7B4%5Csqrt%7B6%7D%7D%7B18%7D%3D%5Cfrac%7B2%5Csqrt%7B6%7D%7D%7B9%7D)
b)![\frac{\sqrt{5}}{5\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{10}}{5*2}=\frac{\sqrt{10}}{10} \frac{\sqrt{5}}{5\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{10}}{5*2}=\frac{\sqrt{10}}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B5%5Csqrt%7B2%7D%7D%2A%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%7B2%7D%7D%3D%5Cfrac%7B%5Csqrt%7B10%7D%7D%7B5%2A2%7D%3D%5Cfrac%7B%5Csqrt%7B10%7D%7D%7B10%7D)
c)![\frac{1}{5+\sqrt{3}}*\frac{5-\sqrt{3}}{{5-\sqrt{3}}}=\frac{5-\sqrt{3}}{5^{2}-\sqrt{3}^{2}}=\frac{5-\sqrt{3}}{25-3}=\frac{5-\sqrt{3}}{22} \frac{1}{5+\sqrt{3}}*\frac{5-\sqrt{3}}{{5-\sqrt{3}}}=\frac{5-\sqrt{3}}{5^{2}-\sqrt{3}^{2}}=\frac{5-\sqrt{3}}{25-3}=\frac{5-\sqrt{3}}{22}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%2B%5Csqrt%7B3%7D%7D%2A%5Cfrac%7B5-%5Csqrt%7B3%7D%7D%7B%7B5-%5Csqrt%7B3%7D%7D%7D%3D%5Cfrac%7B5-%5Csqrt%7B3%7D%7D%7B5%5E%7B2%7D-%5Csqrt%7B3%7D%5E%7B2%7D%7D%3D%5Cfrac%7B5-%5Csqrt%7B3%7D%7D%7B25-3%7D%3D%5Cfrac%7B5-%5Csqrt%7B3%7D%7D%7B22%7D)
d)![\frac{2}{2\sqrt{2}-1}*\frac{2\sqrt{2}+1}{2\sqrt{2}+1}=\frac{4\sqrt{2}+2}{(2\sqrt{2})^{2}-1^{2}}=\frac{4\sqrt{2}+2}{7} \frac{2}{2\sqrt{2}-1}*\frac{2\sqrt{2}+1}{2\sqrt{2}+1}=\frac{4\sqrt{2}+2}{(2\sqrt{2})^{2}-1^{2}}=\frac{4\sqrt{2}+2}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B2%5Csqrt%7B2%7D-1%7D%2A%5Cfrac%7B2%5Csqrt%7B2%7D%2B1%7D%7B2%5Csqrt%7B2%7D%2B1%7D%3D%5Cfrac%7B4%5Csqrt%7B2%7D%2B2%7D%7B%282%5Csqrt%7B2%7D%29%5E%7B2%7D-1%5E%7B2%7D%7D%3D%5Cfrac%7B4%5Csqrt%7B2%7D%2B2%7D%7B7%7D)