\(\sqrt{12+\sqrt{24}+\sqrt{56}+\sqrt{84}}\)
\(=\sqrt{12+2\sqrt{6}+2\sqrt{14}+2\sqrt{21}}\)
\(=\sqrt{2+3+7+2\sqrt{6}+2\sqrt{14}+2\sqrt{21}}\)
\(=\sqrt{2}+\sqrt{3}+\sqrt{7}\)
tính x=\(\sqrt{97-56\sqrt{3}}+\sqrt{52+16\sqrt{3}}\)
y=\(\sqrt{33+20\sqrt{2}}+\sqrt{24-16\sqrt{2}}\)
\(\frac{\sqrt{12}-6}{\sqrt{8}-\sqrt{24}}-\frac{3+\sqrt{3}}{\sqrt{3}}+\frac{4}{1-\sqrt{7}}\)
Thực hiện phép tính:
a) \(\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)
b)\(\sqrt{24-8\sqrt{5}}+\sqrt{9+4\sqrt{5}}\)
c)\(\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}\)
d)\(\sqrt{41+12\sqrt{5}}-\sqrt{46-6\sqrt{5}}\)
e)\(\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)
f)\(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)
g)\(\sqrt{43+24\sqrt{3}}-\sqrt{49-\sqrt{8\sqrt{3}}}\)
h)\(\sqrt{53-20\sqrt{7}}-\sqrt{64+6\sqrt{7}}\)
\(\sqrt{6+\sqrt{24}+\sqrt{12}+\sqrt{8}-\sqrt{3}}=\sqrt{2}+1\)
C/m hằng đẳng thức trên
Bài 1. (2,0 điểm) Thực hiện phép tính: n) 7/9 * sqrt(81) - 1/2 * sqrt(16) . c) (sqrt(8/3) - sqrt(24) + sqrt(50/3)) , sqrt 12 . » sqrt((sqrt(7) - 4) ^ 2) + sqrt(7) 1/(5 + 2sqrt(3)) + 1/(5 - 2sqrt(3))
❤ Tính:
a) \(\sqrt{5-\sqrt{21}}-\sqrt{5+\sqrt{21}}\)
b)\(\sqrt{13-\sqrt{160}}-\sqrt{53+4\sqrt{90}}\)
c)\(\sqrt{7+\sqrt{24}}+\sqrt{31-\sqrt{600}}\)
d)\(\sqrt{28-\sqrt{300}}+\sqrt{4-\sqrt{12}}\)
e)\(\sqrt{7-\sqrt{40}}-\sqrt{5-\sqrt{24}}-\sqrt{6-\sqrt{20}}\)
f)\(\sqrt{48-10\sqrt{7+\sqrt{48}}}\)
g) \(\frac{1}{1-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-\frac{1}{\sqrt{4}-\sqrt{5}}+...+\frac{1}{\sqrt{15}-\sqrt{16}}\)
cmr ; \(\sqrt[3]{1+\sqrt{\frac{56}{54}}}+\sqrt[3]{1-\sqrt{\frac{56}{54}}}\)
Bài 1: Rút gọn biểu thức
a) \(A=\sqrt{26+15\sqrt{3}}\)
b) \(B=\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}-\sqrt{2}\)
c) \(C=\sqrt{8-2\sqrt{15}}-\sqrt{8+2\sqrt{15}}\)
d) \(D=\left(\sqrt{6}-2\right)\left(5+\sqrt{24}\right)\sqrt{5-\sqrt{24}}\)
e) \(E=\left(\sqrt{10}-\sqrt{2}\right)\left(\sqrt{3+\sqrt{5}}\right)\)
f) \(F=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
g) \(G=\left(2-\sqrt{3}\right)\sqrt{26+15\sqrt{3}}-\left(2+\sqrt{3}\right)\sqrt{26-15\sqrt{3}}\)
h) \(H=\frac{\left(2+\sqrt{3}\right)\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\)
Tính:
\(a)\frac{1}{\sqrt{7-\sqrt{24}}+1}+\frac{1}{\sqrt{7+\sqrt{24}}-1}\\ b)\frac{1}{1+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{9}}+...+\frac{1}{\sqrt{2014}+\sqrt{2015}}\)
