a,
$A=\sqrt[]{8-4.\sqrt[]3}-\sqrt[]{8+4.\sqrt[]3}$
$=\sqrt[]{6-2.2.\sqrt[]3+2}-\sqrt[]{6+2.2.\sqrt[]3+2}$
$=\sqrt[]{6-2.\sqrt[]2.\sqrt[]6+2}-\sqrt[]{6+2.\sqrt[]2.\sqrt[]6+2}$
$=\sqrt[]{(\sqrt[]6-\sqrt[]2)^2}-\sqrt[]{(6+\sqrt[]2)^2}$
$=6-\sqrt[]2-6-\sqrt[]2$
$=-2.\sqrt[]2$
b, $B=\sqrt[3]{1+\dfrac{\sqrt[]{84}}{9}}+\sqrt[3]{1-\dfrac{\sqrt[]{84}}{9}}$
Câu này không rút gọn, phía sau sẽ có câu "là nghiệm của pt ...."
nên hướng làm như sau:
$B^3=(\sqrt[3]{1+\dfrac{\sqrt[]{84}}{9}}+\sqrt[3]{1-\dfrac{\sqrt[]{84}}{9}})^3$
$=1+\dfrac{\sqrt[]{84}}{9}+1-\dfrac{\sqrt[]{84}}{9}+3.\sqrt[3]{(1+\dfrac{\sqrt[]{84}}{9}).(1-\dfrac{\sqrt[]{84}}{9})}.(\sqrt[3]{1+\dfrac{\sqrt[]{84}}{9}}+\sqrt[3]{1-\dfrac{\sqrt[]{84}}{9}})$
$=2+3.\sqrt[3]{1-\dfrac{84}{81}}.(\sqrt[3]{1+\dfrac{\sqrt[]{84}}{9}}+\sqrt[3]{1-\dfrac{\sqrt[]{84}}{9}})$
$=2+3.\sqrt[3]{\dfrac{-1}{27}}.(\sqrt[3]{1+\dfrac{\sqrt[]{84}}{9}}+\sqrt[3]{1-\dfrac{\sqrt[]{84}}{9}})$
$=2+3.\dfrac{-1}{3}.(\sqrt[3]{1+\dfrac{\sqrt[]{84}}{9}}+\sqrt[3]{1-\dfrac{\sqrt[]{84}}{9}})$
$=2-(\sqrt[3]{1+\dfrac{\sqrt[]{84}}{9}}+\sqrt[3]{1-\dfrac{\sqrt[]{84}}{9}})$
$=2-B$
