Usun niewymiernosc z mianownika
a.) 3√7/ 2√3
b.) 8-√2/ 5√2
c.) √3-√13 / 3√13
d.) 3 /4-√3
e.) 2√5/√3+√7
f.) 3√3 +2√5 / 3√5-2√2
jakby co to tu nie ma zadnych ulamkow / to kreska ulamkowa ;> proszę bardzo o pelne rozwiazania ;))
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a)![\frac{3\sqrt{7}}{2\sqrt{3}}*\frac{2\sqrt{3}}{2\sqrt{3}}=\frac{6\sqrt{21}}{4\sqrt{9}}=\frac{6\sqrt{21}}{2*3}}=\frac{6\sqrt{21}}{6}}={\sqrt{21} \frac{3\sqrt{7}}{2\sqrt{3}}*\frac{2\sqrt{3}}{2\sqrt{3}}=\frac{6\sqrt{21}}{4\sqrt{9}}=\frac{6\sqrt{21}}{2*3}}=\frac{6\sqrt{21}}{6}}={\sqrt{21}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5Csqrt%7B7%7D%7D%7B2%5Csqrt%7B3%7D%7D%2A%5Cfrac%7B2%5Csqrt%7B3%7D%7D%7B2%5Csqrt%7B3%7D%7D%3D%5Cfrac%7B6%5Csqrt%7B21%7D%7D%7B4%5Csqrt%7B9%7D%7D%3D%5Cfrac%7B6%5Csqrt%7B21%7D%7D%7B2%2A3%7D%7D%3D%5Cfrac%7B6%5Csqrt%7B21%7D%7D%7B6%7D%7D%3D%7B%5Csqrt%7B21%7D)
b)![\frac{8-\sqrt{2}}{5\sqrt{2}}*\frac{5\sqrt{2}}{5\sqrt{2}}=\frac{40\sqrt{2}-5\sqrt{4}}{5^{2}(\sqrt{2})^{2}}=\frac{35\sqrt{2}}{5*2}={35\sqrt{2}}:10={3,5\sqrt{2}} \frac{8-\sqrt{2}}{5\sqrt{2}}*\frac{5\sqrt{2}}{5\sqrt{2}}=\frac{40\sqrt{2}-5\sqrt{4}}{5^{2}(\sqrt{2})^{2}}=\frac{35\sqrt{2}}{5*2}={35\sqrt{2}}:10={3,5\sqrt{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B8-%5Csqrt%7B2%7D%7D%7B5%5Csqrt%7B2%7D%7D%2A%5Cfrac%7B5%5Csqrt%7B2%7D%7D%7B5%5Csqrt%7B2%7D%7D%3D%5Cfrac%7B40%5Csqrt%7B2%7D-5%5Csqrt%7B4%7D%7D%7B5%5E%7B2%7D%28%5Csqrt%7B2%7D%29%5E%7B2%7D%7D%3D%5Cfrac%7B35%5Csqrt%7B2%7D%7D%7B5%2A2%7D%3D%7B35%5Csqrt%7B2%7D%7D%3A10%3D%7B3%2C5%5Csqrt%7B2%7D%7D)
zaraz ci wstawie reszte ;D
c)![{\sqrt{3}-{\sqrt{13}/{3\sqrt{13}*{3\sqrt{13}/{3\sqrt{13} = {\sqrt{39}-{3\sqrt{169}/{9*13}={\sqrt{39}-3*13/117={\sqrt{39}-69/117 {\sqrt{3}-{\sqrt{13}/{3\sqrt{13}*{3\sqrt{13}/{3\sqrt{13} = {\sqrt{39}-{3\sqrt{169}/{9*13}={\sqrt{39}-3*13/117={\sqrt{39}-69/117](https://tex.z-dn.net/?f=%7B%5Csqrt%7B3%7D-%7B%5Csqrt%7B13%7D%2F%7B3%5Csqrt%7B13%7D%2A%7B3%5Csqrt%7B13%7D%2F%7B3%5Csqrt%7B13%7D+%3D+%7B%5Csqrt%7B39%7D-%7B3%5Csqrt%7B169%7D%2F%7B9%2A13%7D%3D%7B%5Csqrt%7B39%7D-3%2A13%2F117%3D%7B%5Csqrt%7B39%7D-69%2F117)
d)![{3}/{4-\sqrt{3}*{4-\sqrt{3}/{4-\sqrt{3}=12-{3\sqrt{3}/{16-3}=12-{3\sqrt{3}/13 {3}/{4-\sqrt{3}*{4-\sqrt{3}/{4-\sqrt{3}=12-{3\sqrt{3}/{16-3}=12-{3\sqrt{3}/13](https://tex.z-dn.net/?f=%7B3%7D%2F%7B4-%5Csqrt%7B3%7D%2A%7B4-%5Csqrt%7B3%7D%2F%7B4-%5Csqrt%7B3%7D%3D12-%7B3%5Csqrt%7B3%7D%2F%7B16-3%7D%3D12-%7B3%5Csqrt%7B3%7D%2F13)
e)
dalej chyba bedziesz wiedzial jak zrobic podobnie jak wyzej
a ostatanie tak samo robisz tylko musisz pamietac o tym ze jak w mianowniku masz - to gdy bedziesz mnozyl przez ta sama liczbe to musi byc na +