\(P=\sqrt{14+6\sqrt{5}}+\sqrt{14-6\sqrt{5}}\)
\(=\sqrt{3^2+6\sqrt{5}+\sqrt{5}^2}+\sqrt{3^2-6\sqrt{5}+\sqrt{5}^2}\)
\(=\sqrt{\left(3+\sqrt{5}\right)^2}+\sqrt{\left(3-\sqrt{5}\right)^2}\)
\(=\left|3+\sqrt{5}\right|+\left|3-\sqrt{5}\right|\)
\(=3+\sqrt{5}+3-\sqrt{5}\)
\(=6\)
RÚT GON BIỂU THỨC
\(\sqrt{14+6\sqrt{5}}-\sqrt{\frac{\sqrt{5}-2}{\sqrt{5}+2}}\)
rút gọn các biểu thức sau
a) \(\sqrt{5+2\sqrt{ }6}+\sqrt{14-4\sqrt{ }6}\)
b) \(\sqrt{5-2\sqrt{ }6}+\sqrt{11-4\sqrt{ }6}\)
c) phân tích 11-\(\sqrt{33}\) thành nhân tử
Gỉai giúp mk vs
\(\sqrt{21-6\sqrt{6}}\)
\(\sqrt{14-6\sqrt{5}}+\sqrt{14+6\sqrt{5}}\)
\(\left(3-\sqrt{2}\right)\sqrt{7+4\sqrt{3}}\)
\(\sqrt{13+4\sqrt{10}}+\sqrt{13-4\sqrt{10}}\)
\(\sqrt{6}\left(\sqrt{26+15\sqrt{3}}+\sqrt{26-15\sqrt{3}}\right)\)
\(\frac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}\)
Tính giá trị biểu thức:
rút gọn các biểu thức sau:
\(\frac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}\)
Tính giá trị biểu thức: \(\dfrac{\sqrt{2}+\sqrt{5-\sqrt{14}}}{\sqrt{12}}\)
rút gọn:
\(\left(5+\sqrt{21}\right)\left(\sqrt{14}-\sqrt{6}\right)\sqrt{5-\sqrt{21}}\)
Rút gọn căn bậc hai theo hằng đẳng thức:
a)\(\left(4\sqrt{2}+\sqrt{30}\right).\left(\sqrt{5}-\sqrt{3}\right)\sqrt{4-\sqrt{15}}\)
b)\(2.\left(\sqrt{10}-\sqrt{2}\right).\left(4+\sqrt{6-2\sqrt{5}}\right)\)
c)\(\left(7+\sqrt{14}\right).\sqrt{9-2\sqrt{14}}\)
d)\(\sqrt{\dfrac{289+4\sqrt{72}}{16}}\)
e) \(\left(\sqrt{21}+7\right).\sqrt{10-2\sqrt{21}}\)
f)\(\sqrt{2-\sqrt{3}.\left(\sqrt{6}+\sqrt{2}\right)}\)
g) \(\sqrt{2}\sqrt{8+3\sqrt{7}}\)
h) \(\sqrt{11+6\sqrt{2}}\)
a,\(\sqrt{14+6\sqrt{5}}+\sqrt{\left(3-\sqrt{5}\right)^2}\)
b,\(\left(\sqrt{6}+\sqrt{2}\right)\sqrt{2-\sqrt{3}}\)
c,\(\frac{2}{\sqrt{3}-1}-\frac{3+\sqrt{3}}{\sqrt{3}+1}\)
