\(\left(2-\sqrt{3}\right)\sqrt{7+4\sqrt{3}}=\left(2-\sqrt{3}\right)\sqrt{2^2+2.2\sqrt{3}+3}=\left(2-\sqrt{3}\right)\sqrt{\left(2+\sqrt{3}\right)^2}\)
\(=\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)=4-3=1\)
\(\sqrt{9-\sqrt{17}}\sqrt{9+\sqrt{17}}=\sqrt{\left(9-\sqrt{17}\right)\left(9+\sqrt{17}\right)}\)
\(=\sqrt{81-17}=\sqrt{64}=8\)
CMR:
a) \(9+4\sqrt{5}=\left(\sqrt{5}+2\right)^2\)
b) \(\sqrt{9-4\sqrt{5}}-\sqrt{5}=-2\)
c) \(23-8\sqrt{7}=\left(4-\sqrt{7}\right)^2\)
d) \(\sqrt{17-12\sqrt{2}}+2\sqrt{2}=3\)
a) \(\sqrt{17-4\sqrt{9+4\sqrt{5}}}\)
b)\(\sqrt{\left(\sqrt{2-3}\right)^2}.\sqrt{11+6\sqrt{2}}\)
c) \(\sqrt{\left(\sqrt{3-3}\right)^2.}\sqrt{\frac{1}{3-\sqrt{3}}}\)
d)\(\left(\sqrt{6}-3\sqrt{3}+5\sqrt{2}-\frac{1}{2}\sqrt{8}\right).2\sqrt{6}\)
rút gọn K
K = \(\sqrt{9-\sqrt{17}}.\sqrt{9+\sqrt{17}}-\sqrt{\left(-8\right)^2}\)
Tính
a)\(\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\)
b)\(\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}\)
c) \(\sqrt{17-12\sqrt{2}}-\sqrt{24-8\sqrt{8}}\)
d)\(\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}\)
Chứng minh :
a) \(9+4\sqrt{5}=\left(\sqrt{5}+2\right)^2\)
b) \(\sqrt{9-4\sqrt{5}}-\sqrt{5}=-2\)
c) \(\left(4-\sqrt{7}\right)^2=23-8\sqrt{7}\)
d) \(\sqrt{23+8\sqrt{7}}-\sqrt{7}=4\)
tính:
a,\(\sqrt{9-4\sqrt{5}}-\sqrt{5}\)
b,\(\sqrt{7-4\sqrt{3}}+\sqrt{4-2\sqrt{3}}\)
c,\(\dfrac{x-49}{\sqrt{x}-7}\)
d,\(\sqrt{4+2\sqrt{3}}-\sqrt{13+4\sqrt{3}}\)
e,\(2+\sqrt{17-4\sqrt{9+4\sqrt{45}}}\)
1)chứng minh
a)\(11+6\sqrt{2}=\left(3+\sqrt{2}\right)^2\)
b)\(\sqrt{11+6\sqrt{2}}+\sqrt{11-6\sqrt{2}}=6\)
2)chứng minh
a)\(8-2\sqrt{7}=\left(\sqrt{7}-1\right)^2\)
b)\(\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}=2\)
Giải hộ ạ!!
a. \(\sqrt{23+8\sqrt{7}}-\sqrt{7}\)
b.\(\sqrt{9-4\sqrt{5}}-\sqrt{5}\)
c. \(\sqrt{\left(3-\sqrt{5}\right)^2}-\sqrt{\left(1-\sqrt{5}\right)^2}\)
bài 1:rút gọn biểu thức:
a)\(\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}\)
b)\(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\)
c)\(\left(\frac{2}{\sqrt{3}-1}+\frac{3}{\sqrt{3}-2}+\frac{15}{3-\sqrt{3}}\right)\times\frac{1}{\sqrt{3}+5}\)
d)\(2\sqrt{40\sqrt{12}}+3\sqrt{5\sqrt{48}}-2\sqrt{\sqrt{75}}-4\sqrt{15\sqrt{27}}\)
bài 2:giải phương trình
a)\(\sqrt{9-12\chi+4\chi^2}=4\)
b)\(\sqrt{\chi^2-2\chi+1}+\sqrt{\chi^2-6\chi+9}=1\)
GIÚP EM VỚI EM ĐANG CẦN GẤP Ạ!!!!!!!!!!!!!!!!!
