Có: \(\left(\sqrt{30+12\sqrt{6}}-\sqrt{30-12\sqrt{6}}\right)^2\)
\(=30+12\sqrt{6}-2\sqrt{\left(30+12\sqrt{6}\right)\left(30-12\sqrt{6}\right)}+30-12\sqrt{6}\)
\(=60-2\sqrt{30^2-12^2\cdot6}\) (hằng đẳng thức số 3)
\(=60-2\sqrt{36}=60-2\cdot6=60-12=48\)
=>\(\sqrt{30+12\sqrt{6}}-\sqrt{30-12\sqrt{6}}=\sqrt{48}=4\sqrt{3}\)
Rút gọn các bt sau
1.\(\sqrt{7+2\sqrt{10}}-\sqrt{7-2\sqrt{10}}\)
2.\(\sqrt{12-6\sqrt{3}+\sqrt{21-12\sqrt{3}}}\)
3.\(\sqrt{33-12\sqrt{6}}+\sqrt{15-6\sqrt{6}}\)
thực hiện phép tính
a, \(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
b,\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{3}}}}\)
c,\(\left(\sqrt{3}-\sqrt{2}\right)\sqrt{5+2\sqrt{6}}\)
d,\(\sqrt{5-\sqrt{13+4\sqrt{3}}+}\sqrt{3+\sqrt{13+4\sqrt{3}}}\)
có ai giúp tui
\(\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{3}-2\right)\sqrt{3}+2\)
\(\frac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\frac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\)
\(2\sqrt{5}-\sqrt{125}-\sqrt{80}+\sqrt{605}\)
\(\sqrt{8\sqrt{3}-2\sqrt{25\sqrt{12}}+8\sqrt{\sqrt{192}}}\)
2. cho A=\(\sqrt{15a^2-8a\sqrt{15}+16}\)
a. Rút gọn A
b. Tính A khi a=\(\sqrt{\frac{3}{5}}+\sqrt{\frac{5}{3}}\)
Thực hện phép tính
a, \(\frac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\frac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\)
b,\(\frac{\sqrt{3-\sqrt{5}}.\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\)
c, \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
d, \(\left(\frac{\sqrt{6}-\sqrt{2}}{1-\sqrt{3}}-\frac{5}{\sqrt{5}}\right):\frac{1}{\sqrt{5}-\sqrt{2}}\)
Rút gọn :
\(B=\frac{6-6\sqrt{3}}{1-\sqrt{3}}+\frac{3\sqrt{3}+3}{\sqrt{3}+1}\)
\(C=\frac{3+\sqrt{3}}{\sqrt{3}}+\frac{\sqrt{6}-\sqrt{3}}{1-\sqrt{2}}\)
\(D=\frac{\sqrt{10}-\sqrt{2}}{\sqrt{5}-1}+\frac{2-\sqrt{2}}{\sqrt{2}-1}\)
\(E=\frac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}+\frac{1}{2-\sqrt{3}}\)
\(F=\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right)\left(\sqrt{6}+11\right)\)
Tính:
a)\(\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}-\sqrt{2}\)
b)\(\sqrt{6.5+\sqrt{12}}+\sqrt{6.5-\sqrt{12}}+2\sqrt{6}\)
\(\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right)\left(\sqrt{6}+1\right)\)
Bài 1: Tính
A=\(\sqrt{46-6\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)
B=\(\sqrt{13-\sqrt{160}-\sqrt{53+4\sqrt{90}}}\)
C=\(\sqrt{15-6\sqrt{6}}+\sqrt{35-12\sqrt{6}}\)
D=\(\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
E= \(\sqrt{4-\sqrt{7}}+\sqrt{4+\sqrt{7}}\)
F= \(\sqrt{3+\sqrt{11+6\sqrt{2}}}-\sqrt{5+2\sqrt{6}}\)
G=\(\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
Bài 2: so sánh
a) \(\sqrt{24}+\sqrt{45}\) và 12
b) \(\sqrt{37}-\sqrt{15}\) và 2
c) \(\sqrt{16}\) và \(\sqrt{15}\times\sqrt{17}\)
d) 8 và \(\sqrt{15}+\sqrt{17}\)
\(\sqrt{15-\sqrt{216}}+\sqrt{33-12\sqrt{6}}\)
