Oblicz [latex]a) (2sqrt{3}+5)^{2}[/latex] [latex]b) log_28+3log_71[/latex] [latex]c) 25^{2}*(frac{1}{5})*5^{4}*125^{2}[/latex] [latex]d) (5sqrt{2}+sqrt{5}) (5sqrt{2}-sqrt{5})[/latex] [latex]e) sqrt[5]{-32}^{-1}*64^{frac{2}{3}}[/latex]

[latex]a) (2sqrt{3}+5)^{2}=\=(2sqrt{3})^{2}+2 cdot 2sqrt{3} cdot 5 +5^{2}=\=4 cdot 3 +20sqrt{3} + 25=\= 12+20sqrt{3}+25=\=37+20sqrt{3}[/latex]   [latex]b) log_28+3log_71=\= 3+log_71^{3}=\=3+0=3[/latex]   [latex]c) 25^{2} cdot (frac{1}{5}) cdot 5^{4} cdot 125^{2}=\=(5^{2})^{2} cdot 5^{-1} cdot 5^{4} cdot (5^{3})^{2}=\=5^{4} cdot 5^{-1} cdot 5^{4} cdot 5^{6}=\=5^{4+(-1)+4+6}=\=5^{13}[/latex]   [latex]d) (5sqrt{2}+sqrt{5}) (5sqrt{2}-sqrt{5})=\=(5sqrt{2})^{2}-(sqrt{5})^{2}=\=(25 cdot 2) - 5=\=50-5=45[/latex]   [latex]e) sqrt[5]{-32}^{-1} cdot 64^{frac{2}{3}}=\=sqrt[5]{(-2)^{5}}^{-1} cdot (2^{6})^{frac{2}{3}}=\=((-2)^{5})^{frac{1}{5}})^{-1} cdot (2^{2})^{2}=\=(-2)^{5 cdot frac{1}{5} cdot (-1) }cdot 2^{4}=\=(-2)^{-1}cdot 2^{4}=\={-frac{1}{2}} cdot 16 =\= -8[/latex]