Ta có: \(\sqrt{2+\sqrt{3}}+\sqrt{14-5\sqrt{3}}+\sqrt{2}\)
\(=\dfrac{\sqrt{4+2\sqrt{3}}+\sqrt{28-10\sqrt{3}}+2}{\sqrt{2}}\)
\(=\dfrac{\sqrt{3}+1+5-\sqrt{3}+2}{\sqrt{2}}\)
\(=4\sqrt{2}\)
Rút gọn biểu thức :
a) A=\(\sqrt[3]{2+\sqrt{5}}+\sqrt[3]{2-\sqrt{5}}\).
b)B=\(\sqrt[3]{20+14\sqrt{2}}+\sqrt[3]{20-14\sqrt{2}}\)
c) C=\(\sqrt[3]{9+4\sqrt{5}}+\sqrt[3]{9-4\sqrt{5}}.\)
1) (\(5\sqrt{3}+2\sqrt{3}\)) (\(2\sqrt{3}-5\sqrt{2}\))
2) \(\sqrt{5+2\sqrt{ }6}-\sqrt{5-2\sqrt{ }6}\)
3)\(\sqrt{14}-6\sqrt{5}+\sqrt{14+6\sqrt{ }5}\)
chứng minh các đẳng thức sau
a) \(\sqrt[3]{2+\sqrt{5}}+\sqrt[3]{2-\sqrt{5}}=1\)
b) \(\sqrt[3]{20+14\sqrt{2}}-\sqrt[3]{14\sqrt{2}-20}=4\)
\(\sqrt[3]{5\sqrt{2}+7}-\sqrt[3]{5\sqrt{2}-7}=2\)
1/ \(\frac{2}{3-\sqrt{7}}\sqrt{\frac{6\sqrt{2}-2\sqrt{14}}{3\sqrt{2}+\sqrt{14}}}\)
2/ \(\sqrt{6+2\sqrt{\sqrt{5}-\sqrt{13-\sqrt{48}}}}\)
3/ \(\frac{\sqrt{3-2\sqrt{2}}}{\sqrt{17-12\sqrt{2}}}-\frac{\sqrt{3+2\sqrt{2}}}{\sqrt{17+12\sqrt{2}}}\)
4/ \(\frac{24}{\sqrt{7}+1}+\frac{4}{3+\sqrt{7}}-\frac{3}{\sqrt{7}+2}\left(4-\sqrt{7}\right)\)
5/ \(\sqrt{7-3\sqrt{5}}\left(7+3\sqrt{5}\right)\left(3\sqrt{2}+\sqrt{10}\right)\)
Thực hiện phép tính:
\(a,\left(\sqrt{28}-2\sqrt{14}+\sqrt{7}\right)\cdot\sqrt{7}+7\sqrt{8}\)
\(b,\left(\sqrt{8}-3\sqrt{2}+\sqrt{10}\right)\cdot\left(\sqrt{2}-3\sqrt{0.4}\right)\)
\(c,\left(15\sqrt{50}+5\sqrt{200}-3\sqrt{450}\right):\sqrt{10}\)
\(d,\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}\)
\(e,\sqrt{11+6\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)
\(f,\sqrt[3]{5\sqrt{2}+7}-\sqrt[3]{5\sqrt{2}-7}\)
\(g,\sqrt[3]{20+14\sqrt{2}}+\sqrt[3]{20-14\sqrt{2}}\)
\(h,\sqrt[3]{26+15\sqrt{3}}-\sqrt[3]{26-15\sqrt{3}}\)
Tính:
1) \(\sqrt{14-2\sqrt{33}}\)
2) \(\sqrt{12-2\sqrt{35}}\)
3) \(\sqrt{16-2\sqrt{55}}\)
4) \(\sqrt{14-6\sqrt{5}}\)
5) \(\sqrt{17-12\sqrt{2}}\)
6) \(\sqrt{27-12\sqrt{5}}\)
7) \(\sqrt{4+\sqrt{15}}\)
LÀM CHI TIẾT GIÚP MK NHÉ!
Rút gọn
a)\(\left(\sqrt{10}+3\sqrt{2}\right)\)\(\sqrt{14-6\sqrt{5}}\)
b)\(\sqrt{3-\sqrt{5}}.\sqrt{3+\sqrt{5}}\)
Rút gọn:
a) \(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)
b) \(\sqrt{\left(3+\sqrt{5}\right)^2}+\sqrt{14-6\sqrt{5}}\)
c) \(\dfrac{3}{2\sqrt{3}+3}+\dfrac{3}{2\sqrt{3}-3}\)
d) \(\sqrt{\left(\sqrt{3}+4\right)\sqrt{19-8\sqrt{3}}+3}\)
e) \(\dfrac{9-2\sqrt{3}}{3\sqrt{6}-2\sqrt{2}}+\dfrac{3}{3+\sqrt{6}}\)
Câu 3: Rút gọn biểu thức sau:
a. \(\dfrac{1}{\sqrt{5}-1}+\dfrac{1}{1+\sqrt{5}}\)
b. \(\sqrt{14-6\sqrt{5}}+\sqrt{\left(2-\sqrt{5}\right)^2}\)
c. \(\dfrac{2}{\sqrt{5}+\sqrt{3}}-\dfrac{3-\sqrt{15}}{\sqrt{5}-\sqrt{3}}\)
