Cześć!
a)
[tex]8\sqrt3+\sqrt{27}=8\sqrt3+\sqrt{9\cdot3}=8\sqrt3+\sqrt{3^2\cdot3}=8\sqrt3+3\sqrt3=11\sqrt3\\[/tex]
b)
[tex]7\sqrt5-\sqrt{125}=7\sqrt5-\sqrt{25\cdot5}=7\sqrt5-\sqrt{5^2\cdot5}=7\sqrt5-5\sqrt2=2\sqrt5\\[/tex]
c)
[tex]\sqrt{48}+\sqrt{12}=\sqrt{16\cdot3}+\sqrt{4\cdot3}=\sqrt{4^2\cdot3}+\sqrt{2^2\cdot3}=4\sqrt3+2\sqrt3=6\sqrt3\\[/tex]
d)
[tex]\sqrt{75}-\sqrt{300}=\sqrt{25\cdot3}-\sqrt{100\cdot3}=\sqrt{5^2\cdot3}-\sqrt{10^2\cdot3}=5\sqrt3-10\sqrt3=-5\sqrt3\\[/tex]
e)
[tex]\sqrt{72}+\sqrt{50}-\sqrt{32}=\sqrt{36\cdot2}+\sqrt{25\cdot2}-\sqrt{16\cdot2}=\\\\=\sqrt{6^2\cdot2}+\sqrt{5^2\cdot2}-\sqrt{4^2\cdot2}=6\sqrt2+5\sqrt2-4\sqrt2=7\sqrt2[/tex]
f)
[tex]\sqrt{20}+\sqrt{45}-\sqrt{500}=\sqrt{4\cdot5}+\sqrt{9\cdot5}-\sqrt{100\cdot5}=\\\\=\sqrt{2^2\cdot5}+\sqrt{3^2\cdot5}-\sqrt{10^2\cdot5}=2\sqrt5+3\sqrt5-10\sqrt5=-5\sqrt5[/tex]
