USUŃ NIEWYMIERNOŚĆ Z MIANOWNIKA UŁAMKA a) [latex] frac{15}{ sqrt{20} } [/latex] b)[latex] frac{10}{ sqrt{3}+1 } [/latex] c)[latex] frac{ sqrt{5} }{3-10} [/latex] d)[latex] frac{ sqrt{2}-1 }{ sqrt{ sqrt{2}+1 } } [/latex]

[latex]a) frac{15}{sqrt{20}}=frac{15}{sqrt{4cdot5}}=frac{15}{2sqrt5}cdotfrac{sqrt5}{sqrt5}=frac{15sqrt5}{2cdot5}=frac{3sqrt5}{2}\\b) frac{10}{sqrt3+1}cdotfrac{sqrt3-1}{sqrt3-1}=frac{10(sqrt3-1)}{(sqrt3)^2-1^2}=frac{10(sqrt3-1)}{3-1}=frac{10(sqrt3-1)}{2}=5(sqrt3-1)[/latex] [latex]c) frac{sqrt5}{3-sqrt{10}}cdotfrac{3+sqrt{10}}{3+sqrt{10}}=frac{3sqrt5+sqrt{50}}{3^2-(sqrt{10})^2}=frac{3sqrt5+sqrt{25cdot2}}{9-10}=frac{3sqrt5+5sqrt2}{-1}=-3sqrt5-5sqrt2\\d) frac{sqrt2-1}{sqrt{sqrt2+1}}cdotfrac{sqrt2-1}{sqrt2-1}=frac{(sqrt2-1)^2}{sqrt{(sqrt2)^2-1^2}}=frac{(sqrt2)^2-2cdotsqrt2cdot1+1^2}{sqrt{2-1}}=frac{2-2sqrt2+1}{sqrt1}=3-2sqrt2[/latex] ©DRK