[tex]zad.1\\\\a)~~\sqrt{225} =\sqrt{15\cdot 15 } =\sqrt{15^{2} } =(15^{2} )^{\frac{1}{2} } =15^{2\cdot \frac{1}{2} } =15^{1} =15\\\\b)~~\sqrt{\dfrac{16}{81} } =\sqrt{\dfrac{4^{2} }{9^{2} } }=\sqrt{(\dfrac{4}{9} )^{2} } =(\dfrac{4}{9} ^{2} )^{\frac{1}{2} } =(\dfrac{4}{9} )^{2\cdot \frac{1}{2} } =(\dfrac{4}{9}) ^{1} =\dfrac{4}{9}\\\\[/tex]
[tex]c)~~\sqrt{4\dfrac{21}{25} } = \sqrt{\dfrac{121}{25} } =\sqrt{\dfrac{11^{2} }{5^{2} } }=\sqrt{(\dfrac{11}{5} )^{2} } =(\dfrac{11}{5} ^{2} )^{\frac{1}{2} } =(\dfrac{11}{5} )^{2\cdot \frac{1}{2} } =(\dfrac{11}{5}) ^{1} =\dfrac{11}{5}=2\dfrac{1}{5}=2,2[/tex]
[tex]d)~~\sqrt{0,0081} =\sqrt{\dfrac{81}{10000} } =\sqrt{\dfrac{9^{2} }{100^{2} } }=\sqrt{(\dfrac{9}{100} )^{2} } =(\dfrac{9}{100} ^{2} )^{\frac{1}{2} } =(\dfrac{9}{100} )^{2\cdot \frac{1}{2} } =(\dfrac{9}{100}) ^{1} =\dfrac{9}{100}=0,09[/tex]
korzystam ze wzoru:
[tex]\sqrt[n]{x^{n} } =(x^{n} )^{\frac{1}{n} } =x^{1} =x[/tex]
