a) -90/189 + 45/84 - 78/126

= -10/21 + 15/28 - 13/21

= (-10/21 - 13/21) + 15/28

= -24/21 + 15/28

= -17/28

\(A=\sqrt[3]{2^3+3.2^2.\sqrt{2}+3.2.\sqrt{2}^2+\sqrt{2}^3}+\sqrt[3]{\sqrt{2}^3-3.\sqrt{2}^2.2+3.\sqrt{2}.2^2-2^3}\)

\(A=\sqrt[3]{\left(2+\sqrt{2}\right)^3}+\sqrt[3]{\left(\sqrt{2}-2\right)^3}\)

\(A=2+\sqrt{2}+\sqrt{2}-2=2\sqrt{2}\)

\(X=\sqrt[3]{1+\frac{\sqrt{84}}{9}}+\sqrt[3]{1-\frac{\sqrt{84}}{9}}\)

\(\Rightarrow X^3=\left(\sqrt[3]{1+\frac{\sqrt{84}}{9}}+\sqrt[3]{1-\frac{\sqrt{84}}{9}}\right)^3\)

\(\Rightarrow X^3=2+3\sqrt[3]{1-\frac{84}{81}}\left(\sqrt[3]{1+\frac{\sqrt{84}}{9}}+\sqrt[3]{1-\frac{\sqrt{84}}{9}}\right)\)

\(\Rightarrow X^3=2-3\sqrt[3]{\frac{1}{27}}.X\)

\(\Rightarrow X^3=2-X\)

\(\Rightarrow X^3+X-2=0\)

\(\Rightarrow\left(X-1\right)\left(X^2+2X+2\right)=0\)

\(\Rightarrow X=1\) (do \(X^2+2X+2=\left(X+1\right)^2+1>0\) \(\forall X\))

a) \(\left(\sqrt{28}-2\sqrt{3}+\sqrt{7}\right)\sqrt{7}+\sqrt{84}\)

\(=\left(2\sqrt{7}-2\sqrt{3}+\sqrt{7}\right)\sqrt{7}+2\sqrt{21}\)

\(=\left(3\sqrt{7}-2\sqrt{3}\right)\sqrt{7}+2\sqrt{21}\)

\(=21-2\sqrt{21}+2\sqrt{21}\)

\(=21\)

b) \(\dfrac{\sqrt{4-2\sqrt{3}}}{\sqrt{6}-\sqrt{2}}\)

\(=\dfrac{\sqrt{\left(\sqrt{3}\right)^2-2\sqrt{3}\cdot1+1^2}}{\sqrt{6}-\sqrt{2}}\)

\(=\dfrac{\sqrt{\left(\sqrt{3}-1\right)^2}}{\sqrt{6}-\sqrt{2}}\)

\(=\dfrac{\left|\sqrt{3}-1\right|}{\sqrt{2}\left(\sqrt{3}-1\right)}\)

\(=\dfrac{\sqrt{3}-1}{\sqrt{2}\left(\sqrt{3}-1\right)}\)

\(=\dfrac{1}{\sqrt{2}}\)

\(\left(\sqrt{7}-\sqrt{3}\right)^2+\sqrt{84}\)

⇔ \(\left(\sqrt{7}\right)^2-2.\sqrt{7}.\sqrt{3}+\left(\sqrt{3}\right)^2+\sqrt{84}\)

⇔ \(7-2\sqrt{21}+3+2\sqrt{21}\)

⇔  \(10\)

a) \(\sqrt{0,16}+\sqrt{0,04}-\sqrt{0,25}\)

= 0,4 + 0,2 - 0,5 

= 0,1

b) \(\sqrt{85^2-84^2}-\sqrt{26^2-24^2}\)

= \(\sqrt{\left(85-84\right)\left(85+84\right)}\) - \(\sqrt{\left(26-24\right)\left(26+24\right)}\)

= \(\sqrt{169}\) - \(\sqrt{2.50}\)

= 13 - 10

= 3 

 Chúc bạn học tốt

a) Ta có: \(\sqrt{0.16}+\sqrt{0.04}-\sqrt{0.25}\)

\(=0,4+0,2-0,5\)

=0,1

b) Ta có: \(\sqrt{85^2-84^2}-\sqrt{26^2-24^2}\)

=13-10

=3

\(\left(\sqrt{28}-2\sqrt{3}+\sqrt{7}\right)\sqrt{7}+\sqrt{84}\)

\(=\sqrt{196}-\sqrt{84}+7+\sqrt{84}\)

\(=14+7=21\)

mk không chép đề

(2\(\sqrt{7}\)-2\(\sqrt{3}\)+\(\sqrt{7}\))\(\sqrt{7}\) +2\(\sqrt{21}\)

=14 -2\(\sqrt{21}\)+7 +2\(\sqrt{21}\)

=21

b: \(=\left(5+\sqrt{21}\right)\left(\sqrt{7}-\sqrt{3}\right)\sqrt{10-2\sqrt{21}}\)

\(=\left(5+\sqrt{21}\right)\left(10-2\sqrt{21}\right)\)

\(=50-10\sqrt{21}+10\sqrt{21}-42=8\)

a: \(A=\sqrt{\sqrt{2}-1}+\sqrt{\sqrt{2}+1}\)

=>\(A^2=\sqrt{2}-1+\sqrt{2}+1+2\sqrt{2-1}=2\sqrt{2}+2\)

=>\(A=\sqrt{2\sqrt{2}+2}\)

Đặt \(B=\sqrt{\sqrt{2}-1}+\sqrt{\sqrt{2}+1}-\sqrt{2+\sqrt{2}}\)

=>\(B=\sqrt{2\sqrt{2}+2}-\sqrt{2+\sqrt{2}}\)

=>\(B^2=2\sqrt{2}+2+2+\sqrt{2}-2\sqrt{\sqrt{2}\left(2+\sqrt{2}\right)\left(2+\sqrt{2}\right)}\)

=>\(B^2=4+3\sqrt{2}-2\sqrt[4]{2}\left(2+\sqrt{2}\right)\)

=>\(B\simeq0,35\)