[tex]zad.1\\\\a)~~\sqrt{64} +\sqrt{144} +\sqrt{196} =\sqrt{8^{2} } +\sqrt{12^{2}} +\sqrt{14^{2} } =8+12+14=34\\\\b)~~\sqrt{625} -\sqrt{225} =\sqrt{15^{2} } -\sqrt{15^{2} } =25-15=10\\\\zad.2\\\\\sqrt{(\dfrac{1}{3} )^{2} } =\dfrac{1}{3} =\dfrac{100}{300} \\\\(\sqrt{0,5^{2} } )^{2} =(0,5)^{2} =0,25=\dfrac{25}{100} =\dfrac{75}{300} \\\\(\sqrt{0,36} )^{2} =0,36=\dfrac{36}{100} =\dfrac{108}{300} \\\\(\sqrt{0,5^{2} } )^{2}~~ < ~~\sqrt{(\dfrac{1}{3} )^{2} } ~~ < ~~(\sqrt{0,36} )^{2}\\\\[/tex]
[tex]zad.3\\\\\sqrt{\dfrac{121}{25} } =\sqrt{(\dfrac{11}{5} )^{2} } =\dfrac{11}{5}=2\dfrac{1}{5}~~liczba~~wymierna\\\\\sqrt{0,04} =\sqrt{\dfrac{4}{100} } =\sqrt{(\dfrac{2}{10} )^{2} } =\dfrac{2}{10}=\dfrac{1}{5} ~~liczba~~wymierna\\\\\sqrt{676}=\sqrt{26^{2} } =26 ~~liczba~~calkowita\\\\\sqrt{\dfrac{1}{6} } =\sqrt{\dfrac{1^{2} }{6} }=\dfrac{\sqrt{1^{2} } }{\sqrt{6} } =\dfrac{1}{\sqrt{6} } \cdot \dfrac{\sqrt{6} }{\sqrt{6} } =\dfrac{\sqrt{6} }{6} ~~liczba~~niewymierna\\\\Odp:~~A.~~jedna[/tex]
Liczba niewymierna - to taka liczba, której nie można zapisać w postaci ułamka zwykłego czyli zapisać w postaci iloraz dwóch liczb całkowitych.
Korzystam ze wzorów:
[tex]\sqrt{x^{2} } =(x^{2} )^{\frac{1}{2} } =x^{2\cdot \frac{1}{2} } =x^{1} =x\\\\( \sqrt{x^{2} } ) ^{2} =( (x^{2} )^{\frac{1}{2} }) ^{2} =x^{2\cdot \frac{1}{2}\cdot 2 }=x^{2}[/tex]
