\(\sqrt{23+4\sqrt{15}}-^3\sqrt{6\sqrt{3}-10}=\sqrt{20+2.2\sqrt{5}.\sqrt{3}+3}-\sqrt[3]{3\sqrt{3}-3.3+3\sqrt{3}-1}=\sqrt{\left(2\sqrt{5}+\sqrt{3}\right)^2}-\sqrt[3]{\left(\sqrt{3}-1\right)^2}=2\sqrt{5}+\sqrt{3}-\sqrt{3}+1=2\sqrt{5}+1\)
Rút gọn các biểu thức sau :
a/\(\sqrt{4-\sqrt{15}} -\sqrt{2+\sqrt{3}}\)
b/\(\sqrt{4+\sqrt{15}}+ \sqrt{7-\sqrt{45}}\)
c/\(\sqrt{6+2\sqrt{5-\sqrt{13+4\sqrt{3}}}} -\sqrt{6-2\sqrt{5+\sqrt{13-4\sqrt{3}}}}\)
Tính:
a) \(\left(2\sqrt{5}-\sqrt{7}\right).\left(2\sqrt{5}+\sqrt{7}\right)\)
b)\(\left(\sqrt{5-2\sqrt{6}}+\sqrt{2}\right).\sqrt{3}\)
c)\(\sqrt{7-4\sqrt{3}}+\sqrt{7+4\sqrt{3}}\)
d)\(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)
e)\(\sqrt{3+\sqrt{5}}+\sqrt{3-\sqrt{5}}\)
g)\(\sqrt{8-2\sqrt{15}}-\sqrt{23-4\sqrt{15}}\)
Cho biểu thức
A = \(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}+1}{\sqrt{x}-3}+\frac{3-11\sqrt{x}}{9-x}\left(x\ge0\right),x\ne9\)
a) Rứt gọn biểu thức
Tính thu gọn :
a , \(\sqrt{17-12\sqrt{2}}-\sqrt{17+12\sqrt{2}}\)
b , \(\sqrt{27+12\sqrt{5}}-\sqrt{27-12\sqrt{5}}\)
c , \(\sqrt{15-6\sqrt{6}}+\sqrt{15+\sqrt{6\sqrt{6}}}\)
d , \(\sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}-2\sqrt{3-\sqrt{5}}\)
e , \(\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}\)
f , \(\sqrt{5+\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
Thu gọn B= \(21\left(\sqrt{2+\sqrt{3}}+\sqrt{3-\sqrt{5}}\right)^2-6\left(\sqrt{2-\sqrt{3}}+\sqrt{3+\sqrt{5}}\right)^2-15\sqrt{5}\)
Thu gọn A= \(\left(2-\sqrt{3}\right)\sqrt{26+15\sqrt{3}}-\left(2+\sqrt{3}\right)\sqrt{26-15\sqrt{3}}\)
* Rút gọn biểu thức
a. \(2\sqrt{80}+3\sqrt{45}-\sqrt{245}\)
b. \(\dfrac{3}{2+\sqrt{3}}+\dfrac{13}{4-\sqrt{3}}+\dfrac{6}{\sqrt{3}}\)
c. \(\left(\dfrac{\sqrt{14}-\sqrt{7}}{\sqrt{2}-1}+\dfrac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}\right):\dfrac{1}{\sqrt{7}-\sqrt{5}}\)
d. \(\sqrt{\left(2+\sqrt{3}\right)^2}-\sqrt{28-10\sqrt{3}}\)
- Rút gọn biểu thức
a. \(2\sqrt{80}+3\sqrt{45}-\sqrt{245}\)
b. \(\dfrac{3}{2+\sqrt{3}}+\dfrac{13}{4-\sqrt{3}}+\dfrac{6}{\sqrt{3}}\)
c. \(\left(\dfrac{\sqrt{14}-\sqrt{7}}{\sqrt{2}-1}+\dfrac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}\right):\dfrac{1}{\sqrt{7}-\sqrt{5}}\)
d. \(\sqrt{\left(2+\sqrt{3}\right)^2}-\sqrt{28-10\sqrt{3}}\)
Tính (rút gọn)
a) \(\left(\sqrt{3+\sqrt{5}}\right)\left(\sqrt{10}+\sqrt{2}\right)\left(3-\sqrt{5}\right)\)
b) \(\left(4+\sqrt{15}\right)\left(\sqrt{10-\sqrt{6}}\right)\sqrt{4-}\sqrt{15}\)
c) \(\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{3}-2\right)\sqrt{\sqrt{3+2}}\)
d) \(\left(2\sqrt{4+\sqrt{6-2\sqrt{5}}}\right)\left(\sqrt{10}-\sqrt{2}\right)\)
f)\(\sqrt{\dfrac{3-\sqrt{5}}{2-\sqrt{3}}}\)
g)\(\dfrac{\sqrt{2+\sqrt{3}}}{3+\sqrt{3}}\)
h)\(\sqrt{4-\sqrt{15}}+\sqrt{4+\sqrt{15}}-2\sqrt{3-\sqrt{5}}\)
Rút gọn:
a. \(\sqrt{6+\sqrt{24}+\sqrt{12}+\sqrt{8}}-\sqrt{4-2\sqrt{3}}\)
b.\(\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right).\left(\sqrt{6}+11\right)\)
