Lời giải:
Đặt \(A=\sqrt{6+3\sqrt{3}}+\sqrt{6-3\sqrt{3}}\)
\(\Rightarrow A\sqrt{2}=\sqrt{12+6\sqrt{3}}+\sqrt{12-6\sqrt{3}}\)
\(A\sqrt{2}=\sqrt{3^2+3-2.3\sqrt{3}}+\sqrt{3^2+3-2.3\sqrt{3}}\)
\(=\sqrt{(3+\sqrt{3})^2}+\sqrt{(3-\sqrt{3})^2}\)
\(=3+\sqrt{3}+3-\sqrt{3}=6\)
\(\Rightarrow A=\frac{6}{\sqrt{2}}=3\sqrt{2}\)
Rút gọn:
\(A=\sqrt{3+2\sqrt{2}}-\sqrt{6+2\sqrt{2}+2\sqrt{3}+2\sqrt{6}}\)
rút gọn
\(\sqrt{x+12+6\sqrt{x+3}}-\sqrt{x+12-6\sqrt{x+3}}\) ( x>6)
\(\sqrt{7-4\sqrt{3}}\) + \(\sqrt{12+6\sqrt{3}}\)
rút gọn biểu thức trên
rút gọn M=\(\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{3}-2\right)\sqrt{\sqrt{3}+2}\)
( \(\dfrac{3\sqrt{x}+6}{x-4}\) + \(\dfrac{\sqrt{x}}{\sqrt{x}-2}\) ) : \(\dfrac{x-9}{\sqrt{x}-3}\)
rút gọn biểu thức
rút gọn các biểu thức sau:
a,\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
b,\(\sqrt{6+2\sqrt{5}-\sqrt{29-12\sqrt{5}}}\)
c,\(\sqrt{2+\sqrt{5-\sqrt{13-\sqrt{48}}}}\)
d,\(\left(3-\sqrt{5}\right)\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right)\sqrt{3-\sqrt{5}}\)
Rút gọn : P= \(\dfrac{\sqrt{3}}{\sqrt{\sqrt{3}+1}-1}-\dfrac{\sqrt{3}}{\sqrt{\sqrt{3}+1}+1}\)
Rút gọn :C= \(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)
D=\(\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}\)
Rút gọn biểu thức \(\frac{\sqrt{6+2\left(\sqrt{6}+\sqrt{3}+\sqrt{2}\right)}-\sqrt{6-2\left(\sqrt{6}-\sqrt{3}+\sqrt{2}\right)}}{\sqrt{2}}\)
Rút gọn:
\(\frac{\sqrt{8}-\sqrt{6}}{2-\sqrt{3}}+\frac{\sqrt{8}+\sqrt{6}}{2+\sqrt{3}}\)
