Lời giải:
a)
\(\sqrt{8}+\sqrt{50}-\sqrt{288}=\sqrt{2}.\sqrt{4}+\sqrt{2}.\sqrt{25}-\sqrt{2}.\sqrt{144}\)
\(=\sqrt{2}.2+\sqrt{2}.5-\sqrt{2}.12=\sqrt{2}(2+5-12)=-5\sqrt{2}\)
b)
\(\sqrt{4+\sqrt{15}}.\sqrt{4-\sqrt{15}}=\sqrt{(4-\sqrt{15})(4+\sqrt{15})}\)
\(=\sqrt{4^2-(\sqrt{15})^2}=\sqrt{16-15}=1\)
Tính giá trị các biểu thức:
a.\(\left(7\sqrt{48}+3\sqrt{27}-2\sqrt{12}\right)\sqrt{3}\)
b.\(\left(12\sqrt{50}-8\sqrt{200}+7\sqrt{450}\right):\sqrt{10}\)
c.\(\left(2\sqrt{6}-4\sqrt{3}+5\sqrt{2}-\dfrac{1}{4}\sqrt{8}\right)3\sqrt{6}\)
d.\(3\sqrt{15\sqrt{50}}+5\sqrt{24\sqrt{8}}-4\sqrt{12\sqrt{32}}\)
a) \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
b) \(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
Tính
a) \(3\sqrt{2x}-5\sqrt{8x}+7\sqrt{18x}\)
b) \(\left(2\sqrt{3}+4\right)\left(\sqrt{3}-2\right)\)
c) \(\sqrt{3+2\sqrt{2}}+\sqrt{\left(\sqrt{2}-2\right)^2}\)
d) \(\sqrt{4-\sqrt{15}}-\sqrt{4+\sqrt{15}}+\sqrt{6}\)
e) \(\left(\dfrac{5-\sqrt{5}}{\sqrt{5}}-2\right)\left(\dfrac{4}{1+\sqrt{5}}+4\right)\)
f) \(\dfrac{1}{5}\sqrt{50}-2\sqrt{96}-\dfrac{\sqrt{30}}{\sqrt{15}}+12\sqrt{\dfrac{1}{6}}\)
* Rút gọn biểu thức
c.\(\dfrac{1}{2\sqrt{2}}-\dfrac{3}{2}\sqrt{4,5}+\dfrac{2}{5}\sqrt{50}\)
d.\(\dfrac{4}{3+\sqrt{5}}-\dfrac{8}{1+\sqrt{5}}+\dfrac{15}{\sqrt{5}}\)
\(\sqrt{17+4\sqrt{15}}\) - \(\sqrt{8-2\sqrt{15}}\)
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)\(\sqrt{8-2\sqrt{15}}-\sqrt{23-4\sqrt{15}}\)
Tinh:
a)\(\sqrt{\sqrt{2019}+\sqrt{2018}}.\sqrt{\sqrt{2019}-\sqrt{2018}}\)
b)\(\sqrt{4+\sqrt{15}}-\sqrt{4-\sqrt{15}}\)
Rút gọn
A= \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
B= \(\sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}-2\sqrt{3-5}\)
rút gọn
a) \(\sqrt{\left(2-\sqrt{3}\right)^2}\) + \(\sqrt{4-2\sqrt{3}}\)
b) \(\sqrt{15-6\sqrt{5}}\) + \(\sqrt{33-12\sqrt{6}}\)
c) \(\left(15\sqrt{200}-3\sqrt{450}+2\sqrt{50}\right):\sqrt{10}\)
