\(B=\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}\)
\(=\sqrt{5}-\sqrt{3-\sqrt{\left(2\sqrt{5}-3\right)^2}}\)
\(=\sqrt{5}-\sqrt{3-2\sqrt{5}+3}\)
\(=\sqrt{5}-\sqrt{\left(\sqrt{5}-1\right)^2}\)
\(=\sqrt{5}-\sqrt{5}+1\)
\(=1\)
Rut gon :
B= \(\sqrt{\sqrt{5}-\sqrt{3}-\sqrt{29}-12\sqrt{5}}\)
tính H = \(\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}\)
rut gon bieu thuc a) \(\sqrt{15+2\sqrt{5}-\sqrt[]{21-4\sqrt{5}}}\)
b)\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{ }}}5}\)
Bài 1 Rút gọn: D = \(\sqrt{\sqrt{5}-\sqrt{\sqrt{3}-\left(29-12\sqrt{5}\right)}}\)
\(\sqrt{29+12\sqrt{5}}+\sqrt{9-4\sqrt{5}}-3\sqrt{5}\)
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 , \(\sqrt{5+\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
Rút gọn các biểu thức sau:
A =\(\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}\)
B = \(\sqrt{3-\sqrt{5}}.\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\)
1. so sánh
a. 3 + \(\sqrt{5}và\) \(\sqrt{2}+\sqrt{6}\) b. 2 + \(\sqrt{3}\) và \(\sqrt{5+4\sqrt{ }3}\)
c. \(\sqrt{5}+\sqrt{7}\) và \(\sqrt{12+2\sqrt{ }35}\) d. \(\sqrt{2013}\) + \(\sqrt{2015}\) và 2\(\sqrt{2014}\)
2.tính
a. \(\sqrt{14+6\sqrt{ }5}\) + \(\sqrt{14-6\sqrt{ }5}\) b. \(\sqrt{6+4\sqrt{ }2}+\sqrt{11-6\sqrt{ }2}\)
c. \(\sqrt{29-12\sqrt{ }5}-\sqrt{29+12\sqrt{ }5}\) d. \(\sqrt{30+10\sqrt{ }7}+\sqrt{30-10\sqrt{ }7}\)
e.\(\sqrt{30+12\sqrt{ }6}+\sqrt{30-12\sqrt{ }6}\) f. \(\sqrt{4+\sqrt{ }7}-\sqrt{4-\sqrt{ }7}-\sqrt{2}\)