\(=\sqrt{2}.\sqrt{10-2\sqrt{21}}\)
\(=\sqrt{2}.\sqrt{3-2\sqrt{3}.\sqrt{7}+7}\)
\(=\sqrt{2}.\sqrt{\left(\sqrt{3}-\sqrt{7}\right)^2}\)
\(=\sqrt{2}.\left(\sqrt{7}-\sqrt{3}\right)\)
\(=\sqrt{14}-\sqrt{6}\)
\(2\sqrt{5-\sqrt{21}}=\sqrt{4.\left(5-\sqrt{21}\right)}\)
\(=\sqrt{20-4\sqrt{21}}=\sqrt{20-4\sqrt{5}+1}=\sqrt{\left(2\sqrt{5}-1\right)^2}\)
\(=\left|2\sqrt{5}-1\right|=2\sqrt{5}-1\)
Bài: Tính giá trị các biểu thức sau
a. \(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}+\sqrt{2}\right)\)
b. \(\left(\sqrt{21}+7\right).\sqrt{10-2\sqrt{21}}\)
Chứng minh đẳng thức :
a) \(A=\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}=\sqrt{2}\)
b) \(B=\left(5+\sqrt{21}\right)\left(\sqrt{14}-\sqrt{6}\right)\sqrt{5-\sqrt{21}}=8\)
* Chứng minh đẳng thức:
\(\left(\dfrac{14}{\sqrt{14}}+\dfrac{\sqrt{12}+\sqrt{30}}{\sqrt{2}+\sqrt{5}}\right).\sqrt{5-\sqrt{21}}=4\)
Tính A=21 \(\left(\sqrt{2+\sqrt{3}}+\sqrt{3-\sqrt{5}}\right)^2\) -6\(\left(\sqrt{2-\sqrt{3}}+\sqrt{3+\sqrt{5}}\right)^2-15\sqrt{5}\)
Tính: A = \(21\left(\sqrt{2+\sqrt{3}}+\sqrt{3-\sqrt{5}}\right)^2-6\left(\sqrt{2-\sqrt{3}}+\sqrt{3+\sqrt{5}}\right)^2-15\sqrt{15}\)
Rút gọn: \(\left(5+\sqrt{21}\right)\left(\sqrt{14}-\sqrt{6}\right)\sqrt{5-\sqrt{21}}\)
Tính: \(21\sqrt{\frac{3}{7}}-\frac{13}{2\sqrt{3}-5}-\sqrt{21-12\sqrt{3}}\)
Tính:
a,\(\sqrt{19-6\sqrt{2}}\)
b,\(\sqrt{21+12\sqrt{3}}\)
c,\(\sqrt{57-40\sqrt{2}}\)
d,\(\sqrt{\left(5-2\sqrt{6}\right)\left(4-2\sqrt{3}\right)}\)
e,\(\sqrt{21+6\sqrt{6}}+\sqrt{21-6\sqrt{6}}\)
g,\(\sqrt{7-4\sqrt{3}}-\sqrt{7+4\sqrt{3}}\)
rut gon bieu thuc a) \(\sqrt{15+2\sqrt{5}-\sqrt[]{21-4\sqrt{5}}}\)
b)\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
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= \(\left(2-\sqrt{3}\right)\sqrt{26+15\sqrt{3}}-\left(2+\sqrt{3}\right)\sqrt{26-15\sqrt{3}}\)
