Potęgi i pierwiastki 1.28 Oblicz b) √√900+6 - pierwiastek z pierwiastka z 900 + 6 c) √5*(2√125-√5) 1.32 Usuń niewymierność z mianownika ułamka: b) 0,1*√0,02/√2 e) √5-√3/√3 1.33 Doprowadź do najprostszej postaci wyrażenie: a) 4√3+√27 c) 6√50+√32-3

[latex]1.28\ b) sqrt{sqrt{900}+6}=sqrt{30+6}=sqrt{36}=6\ c) sqrt5cdot(2sqrt{125}-sqrt5)=sqrt5(2cdot5sqrt5-sqrt5)=\ =sqrt5(10sqrt5-sqrt5)=sqrt5cdot9sqrt5=9cdot5=45[/latex] [latex]1.32\ b) frac{0,1cdotsqrt{0,02}}{sqrt2}=frac{0,1cdotsqrt{0,02}}{sqrt2}cdotfrac{sqrt2}{sqrt2}=frac{0,1cdotsqrt{0,04}}{2}=frac{0,1cdot0,2}{2}=\ =frac{0,1cdot0,1cdot2}{2}=0,1cdot0,1=0,001\ \ e) frac{sqrt5-sqrt3}{sqrt3}=frac{sqrt5-sqrt3}{sqrt3}cdotfrac{sqrt3}{sqrt3}=frac{sqrt{15}-3}{3}[/latex] [latex]1.33\ a) 4sqrt3+sqrt{27}=4sqrt3+sqrt{9cdot3}=4sqrt3+3sqrt3=7sqrt3\ \ c) 6sqrt{50}+sqrt32-3sqrt{72}=6sqrt{25cdot2}+sqrt{16cdot2}-3sqrt{36cdot2}=\ =6cdot5sqrt2+4sqrt2-3cdot6sqrt2=30sqrt2+4sqrt2-18sqrt2=\ =16sqrt2\ \ d) frac{sqrt{24}-sqrt{54}+sqrt6}{sqrt6}=frac{sqrt{6cdot4}-sqrt{6cdot9}+sqrt6}{sqrt6}=frac{sqrt6(sqrt4-sqrt9+1)}{sqrt6}=\ =sqrt4-sqrt9+1=2-3+1=3-3=0[/latex]