a/ $5\sqrt 4+3\sqrt{25}-\sqrt{64}\\=5\sqrt{2^2}+3\sqrt{5^2}-\sqrt{8^2}\\=5.|2|+3.|5|-|8|\\=5.2+3.5-8\\=10+15-8\\=17$
Vậy $5\sqrt 4+3\sqrt{25}-\sqrt{64}=17$
b/ $\dfrac{1}{2}\sqrt 8+2\sqrt{\dfrac 1 2}-3\sqrt 2\\=\dfrac{1}{2}.\sqrt{4.2}+(\sqrt 2)^2.\dfrac{1}{\sqrt 2}-3\sqrt 2\\=\dfrac{1}{2}.\sqrt 4.\sqrt 2+\sqrt 2-3\sqrt 2\\=\dfrac{1}{2}.\sqrt{2^2}.\sqrt 2-2\sqrt 2\\=\dfrac{1}{2}.|2|\sqrt 2-2\sqrt 2\\=\dfrac{1}{2}.2.\sqrt 2-2\sqrt 2\\=\sqrt 2-2\sqrt2\\=-\sqrt 2$
Vậy $\dfrac{1}{2}\sqrt 8+2\sqrt{\dfrac 1 2}-3\sqrt 2=-\sqrt 2$
c/ $5\sqrt{20}-3\sqrt{12}+\sqrt 5-2\sqrt{27}\\=5\sqrt{4.5}-3\sqrt{3.4}+\sqrt 5-2\sqrt{9.3}\\=5.\sqrt 4.\sqrt 5-3.\sqrt 3.\sqrt 4+\sqrt 5-2.\sqrt 9.\sqrt 3\\=5\sqrt{2^2}.\sqrt 5-3.\sqrt 3.\sqrt{2^2}+\sqrt 5-2.\sqrt{3^2}.\sqrt 3\\=5.|2|.\sqrt 5-3.|2|.\sqrt 3+\sqrt 5-2.|3|.\sqrt 3\\=5.2.\sqrt 5-3.2.\sqrt 3+\sqrt 5-2.3.\sqrt 3\\=10\sqrt 5-6\sqrt 3+\sqrt 5-6\sqrt 3\\=11\sqrt 5-12\sqrt 3$
Vậy $5\sqrt{20}-3\sqrt{12}+\sqrt 5-2\sqrt{27}=11\sqrt 5-12\sqrt 3$
d/ $\sqrt{125}+2+\sqrt{6-2\sqrt 5}\\=\sqrt{25.5}+2+\sqrt{5-2\sqrt 5+1}\\=\sqrt{25}.\sqrt 5+2+\sqrt{(\sqrt 5)^2-2.\sqrt 5.1+1^2}\\=\sqrt{5^2}.\sqrt 5+2+\sqrt{(\sqrt 5-1)^2}\\=|5|.\sqrt 5+2+|\sqrt 5-1|\\=5\sqrt 5+2+(\sqrt 5-1)\\=5\sqrt 5+2+\sqrt 5-1\\=6\sqrt 5+1$
Vậy $\sqrt{125}+2+\sqrt{6-2\sqrt 5}=6\sqrt 5+1$
