Bài 8
$M=\sqrt{16a^2}-5a=|4a|-5a=4a-5a=-a$
$N=\sqrt{25b^2}+3b=|5b|+3b=-5b+3b=-2b$
$P=\sqrt{x^2-10x+25}-x=\sqrt{(x-5)^2}-x=|x-5|-x=x-5-x=-5$
$Q=3x+2-\sqrt{9x^2+6x+1}=3x+2-\sqrt{(3x+1)^2}=3x+2-|3x+1|=3x+2-3x-1=1$
Bài 9
$A=\sqrt{8+2\sqrt{7}}-\sqrt{7}=\sqrt{(\sqrt{7}+1)^2}-\sqrt{7}=|\sqrt{7}+1|-\sqrt{7}=1$
$B=\sqrt{7+4\sqrt{3}}-2\sqrt{3}=\sqrt{(2+\sqrt{3})^2}-2\sqrt{3}=|2+\sqrt{3}|-2\sqrt{3}=2-\sqrt{3}$
$C=\sqrt{14-2\sqrt{13}}+\sqrt{14+2\sqrt{13}}=\sqrt{(1-\sqrt{13})^2}+\sqrt{(1+\sqrt{13})^2}=|1-\sqrt{13}|+|1+\sqrt{13}|=\sqrt{13}-1+1+\sqrt{13}=2\sqrt{13}$
$D=\sqrt{22-2\sqrt{21}}-\sqrt{22+2\sqrt{21}}=\sqrt{(1-\sqrt{21})^2}-\sqrt{(1+\sqrt{21})^2}=|1-\sqrt{21}|-|1+\sqrt{21}|=\sqrt{21}-1-1-\sqrt{21}=-2$
Bài 10
$A=\sqrt{11-6\sqrt{2}}-\sqrt{11+6\sqrt{2}}=\sqrt{(3-\sqrt{2})^2}-\sqrt{(3+\sqrt{2})^2}=|3-\sqrt{2}|-|3+\sqrt{2}|=3-\sqrt{2}-3-\sqrt{2}=-2\sqrt{2}$
$B=\sqrt{(2-\sqrt{5})^2}+\sqrt{14-6\sqrt{5}}=\sqrt{(2-\sqrt{5})^2}+\sqrt{(3-\sqrt{5})^2}=|2-\sqrt{5}|+|3-\sqrt{5}|=\sqrt{5}-2+3-\sqrt{5}=1$
$C=(2+\sqrt{7})\sqrt{11-4\sqrt{7}}=(\sqrt{7}+2)\sqrt{(2-\sqrt{7})^2}=(\sqrt{7}+2)|2-\sqrt{7}|=(\sqrt{7}+2)(\sqrt{7}-2)=7-4=3$
$D=\sqrt{(3+\sqrt{2})^2}+\sqrt{6-4\sqrt{2}}=\sqrt{(3+\sqrt{2})^2}+\sqrt{(2-\sqrt{2})^2}=|3+\sqrt{2}|+|2-\sqrt{2}|=3+\sqrt{2}+2-\sqrt{2}=5$
