Bài 1:Tính giá trị biểu thức sau:
a) A=\(\sqrt{\left(2-\sqrt{5}\right)^2}\) + \(\sqrt{\left(2\sqrt{2}-\sqrt{5}\right)^2}\)
b) B=\(\sqrt{\left(\sqrt{7}-2\sqrt{2}\right)^2}\) + \(\sqrt{\left(3-2\sqrt{2}\right)^2}\)
c) C=\(\sqrt{11+6\sqrt{2}}\) - \(\sqrt{11-6\sqrt{2}}\)
Bài 2: Rút gọn biểu thức:
a) B= 3\(\sqrt{9a^6}\) - \(6a^3\)
b) C=\(\sqrt{a^2+6a+9}\) + \(\sqrt{a^2-6a+9}\) (-3\(\le\)a\(\le\)3)
Bài 1:
a: \(A=\sqrt{\left(2-\sqrt{5}\right)^2}+\sqrt{\left(2\sqrt{2}-\sqrt{5}\right)^2}\)
\(=\left|2-\sqrt{5}\right|+\left|2\sqrt{2}-\sqrt{5}\right|\)
\(=\sqrt{5}-2+2\sqrt{2}-\sqrt{5}=2\sqrt{2}-2\)
b: \(B=\sqrt{\left(\sqrt{7}-2\sqrt{2}\right)^2}+\sqrt{\left(3-2\sqrt{2}\right)^2}\)
\(=\left|\sqrt{7}-2\sqrt{2}\right|+\left|3-2\sqrt{2}\right|\)
\(=2\sqrt{2}-\sqrt{7}+3-2\sqrt{2}=3-\sqrt{7}\)
c: \(C=\sqrt{11+6\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)
\(=\sqrt{\left(3+\sqrt{2}\right)^2}-\sqrt{\left(3-\sqrt{2}\right)^2}\)
\(=3+\sqrt{2}-\left(3-\sqrt{2}\right)=3+\sqrt{2}-3+\sqrt{2}=2\sqrt{2}\)
Bài 2:
a: \(B=3\cdot\sqrt{9a^6}-6a^3=3\cdot3a^3-6a^3=9a^3-6a^3=3a^3\)
b: \(C=\sqrt{a^2+6a+9}+\sqrt{a^2-6a+9}\)
\(=\sqrt{\left(a+3\right)^2}+\sqrt{\left(a-3\right)^2}\)
\(=\left|a+3\right|+\left|a-3\right|\)
-3<=a<=3
=>a+3>=0; a-3<=0
=>\(C=a+3+3-a=6\)
