a/ \(11-\sqrt{33}=\sqrt{11}\left(\sqrt{11}-\sqrt{3}\right)\)
b/ \(2\sqrt{15}-3\sqrt{5}=2\sqrt{15}-\sqrt{3}.\sqrt{15}=\sqrt{15}\left(2-\sqrt{3}\right)\)
c/ \(4x^2-7=\left(2x\right)^2-\left(\sqrt{7}\right)^2=\left(2x-\sqrt{7}\right)\left(2x+\sqrt{7}\right)\)
d/ \(2+x^2-2x\sqrt{2}=x^2-2.x.\sqrt{2}+\left(\sqrt{2}\right)^2=\left(x-\sqrt{2}\right)^2\)
Bài 1:
a) \(\sqrt{13-2\sqrt{42}}\)
b) \(\sqrt{46+6\sqrt{5}}\)
c) \(\sqrt{12-3\sqrt{15}}\)
d) \(\sqrt{11+\sqrt{96}}\)
Bài 2:
a) \(A=\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{4+2\sqrt{3}}}}\)
b) \(B=\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}\)
c) \(C=\sqrt{3-\sqrt{5}}\left(\sqrt{10}+\sqrt{2}\right)\left(3+\sqrt{5}\right)\)
d) \(D=\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\)
e) \(E=\sqrt{8+2\sqrt{10+2\sqrt{5}}}+\sqrt{8-2\sqrt{10+2\sqrt{5}}}\)
g) \(G=\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}\)
h) \(H=4x-\sqrt{9x^2-12x+4}\)
i) \(\frac{\sqrt{7}-\sqrt{2}}{\sqrt{7}+\sqrt{2}}+\frac{\sqrt{7}+\sqrt{2}}{\sqrt{7}-\sqrt{2}}\)
Tính:
a) \(A=\sqrt{8-2\sqrt{15}}\left(\sqrt{3}+\sqrt{5}\right)-\left(\sqrt{45}-\sqrt{20}\right)\)
b) \(B=\left(\frac{\sqrt{21}-\sqrt{3}}{\sqrt{7}-1}-\frac{\sqrt{15}-\sqrt{3}}{1-\sqrt{5}}\right)\left(\frac{1}{2}\sqrt{6}-\sqrt{\frac{3}{2}}+3\sqrt{\frac{2}{3}}\right)\)
c) \(C=2\sqrt{3}+\sqrt{7-4\sqrt{3}}+\left(\sqrt{\frac{1}{3}}-\sqrt{\frac{4}{3}+}\sqrt{3}\right):\sqrt{3}\)
d) \(D=\left(\frac{5+\sqrt{5}}{5-\sqrt{5}}+\frac{5-\sqrt{5}}{5+\sqrt{5}}\right):\frac{1}{\sqrt{7-4\sqrt{3}}}\)
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
rút gọn
a) A=\(\sqrt{4-2\sqrt{3}}-\sqrt{4+2\sqrt{3}}\)
b) B=\(\sqrt{11-6\sqrt{2}}-\sqrt{3-2\sqrt{2}}\)
c) C=\(\left(\sqrt{3}+\sqrt{5}\right)\times\sqrt{7-2\sqrt{10}}\)
lm nhanh giúp mk nhé
phân tích đa thức thành nhân tử
\(x\sqrt{x}-9\)
\(x-\sqrt{x}-6\)
\(2x+5\sqrt{x}-3\)
\(8\sqrt{\frac{2}{5}}+7\sqrt{\frac{5}{2}}-\frac{\sqrt{33}}{\sqrt{3}}+\frac{10}{\sqrt{11}-1}\)
1. Rút gọn \(A=\sqrt{x+\sqrt{2x-1}}-\sqrt{x-\sqrt{2x-1}}\)
2. Tính \(B=\frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}-\sqrt{3-2\sqrt{2}}\)
3.Tính \(C=\frac{\sqrt{3-\sqrt{5}}\cdot\left(\sqrt{10}-\sqrt{2}\right)\cdot\left(3+\sqrt{5}\right)}{\left(4+\sqrt{15}\right)\cdot\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}}\)
Thực hiện phép tính:
a)\(\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)
b)\(\dfrac{\sqrt{7+\sqrt{5}}+\sqrt{7-\sqrt{5}}}{\sqrt{7+\sqrt{11}}}-\sqrt{3-2\sqrt{2}}\)
c)\(\sqrt{8+2\sqrt{10+2\sqrt{5}}}+\sqrt{8-2\sqrt{10+2\sqrt{5}}}\)
a,\(\left(\sqrt{27}-\sqrt{12}-\sqrt{108}-\sqrt{192}\right):\sqrt{3}\)
b,\(\frac{\sqrt{2}-\sqrt{6}}{1-\sqrt{3}}\frac{3+2\sqrt{7}}{1+\sqrt{3}}\)
c,(\(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)
