Ta có: \(\sqrt{19-6\sqrt{2}}\)
\(=\sqrt{18-2\cdot3\sqrt{2}\cdot1+1}\)
\(=\sqrt{\left(3\sqrt{2}-1\right)^2}\)
\(=\left|3\sqrt{2}-1\right|\)
\(=3\sqrt{2}-1\)(Vì \(3\sqrt{2}>1\))
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!!!!!!!!!!!!!!!!!
Bài 1: Tính
\(\sqrt{3+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\\ \sqrt{12+6\sqrt{3}+\sqrt{12-6\sqrt{3}}}\\ \sqrt{9-4\sqrt{2}+\sqrt{9+4\sqrt{2}}}\)
\(\sqrt{\sqrt{2}+2+\sqrt{4+\sqrt{9-\sqrt{32}}}}\\ \sqrt{6+2\sqrt{5}-\sqrt{29+12\sqrt{5}}}\\ \sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}}-\sqrt{\sqrt{49}+\sqrt{40}}\\ \sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
câu 1 : thực hiện phép tính
a) \(\sqrt{50}-\sqrt{54}+\frac{1}{2}\sqrt{72}+\frac{5}{6}\sqrt{216}\)
b) \(\frac{1}{2}\sqrt{48}-\sqrt{32}-\sqrt{75}-\frac{1}{5}\sqrt{50}\)
c)\(\frac{\sqrt{2}-1}{2-\sqrt{2}}\)
d)\(4\sqrt{\frac{3}{2}}-\frac{5}{2}\sqrt{24}+\frac{1}{2}\sqrt{32}\)
e)\(24\sqrt{\frac{2}{3}}+6\sqrt{\frac{3}{2}}-3\sqrt{24}\)
f)\(2\sqrt{12}+3\sqrt{27}-\sqrt{48}\)
g)\(\left(2\sqrt{5}+5\sqrt{2}\right).\sqrt{5}-\sqrt{250}\)
h)\(\frac{3+\sqrt{3}}{3-\sqrt{3}}+\frac{3-\sqrt{3}}{3+\sqrt{3}}\)
k)\(\left(\sqrt{28}-\sqrt{12}+\sqrt{7}\right).\sqrt{7}+2.\sqrt{21}\)
l)\(\frac{2.\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}\)
Ai đó giúp mình với ạ!
1)\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
2)\(\sqrt{35+12\sqrt{6}}-\sqrt{35-12\sqrt{6}}\)
3)\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
1) \(\sqrt{12}-\sqrt{27}+\sqrt{3}\)
2)\(\sqrt{252}-\sqrt{700}+\sqrt{1008}-\sqrt{448}\)
3)\(3\sqrt{112}-7\sqrt{216}+4\sqrt{54}-2\sqrt{252}-3\sqrt{96}\)
4)\(\sqrt{18}-3\sqrt{80}-2\sqrt{50}+2\sqrt{45}\)
5)\(6\sqrt{12}-\sqrt{20}-2\sqrt{27}+\sqrt{125}\)
6)\(2\sqrt{18}-3\sqrt{80}-5\sqrt{147}+5\sqrt{245}-3\sqrt{98}\)
GIÚP MÌNH VỚI
\(a,\sqrt{10+\sqrt{9}}\)
b,\(\sqrt{21+6\sqrt{6}}\)-\(\sqrt{21-6\sqrt{6}}\)
c\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10-2\sqrt{5}}}\)
d,\(\sqrt{x+1+2\sqrt{x}}\)
e,\(\sqrt{2\text{x}+3+2\sqrt{x^2+3\text{x}+2}}\)
giúp mik với,cảm ơn trc ạ
18 - 6\(\sqrt{10}\)
19 + 8\(\sqrt{3}\)
27 + 10\(\sqrt{2}\)
28 + 12\(\sqrt{2}\)
Rút gọn biểu thức.
a)\(\sqrt{3+2\sqrt{2}-\sqrt{3-2\sqrt{2}}}\). c)\(\sqrt{5-2\sqrt{6}}+\sqrt{7+2\sqrt{10}}\)
b)\(\sqrt{7-4\sqrt{3}+\sqrt{12+6\sqrt{3}}}\) d)\(\frac{\sqrt{8-2\sqrt{12}}}{\sqrt{3}-1}\)-\(\sqrt{8}\)
thực hiện phép tính
a)\(\sqrt{6+2\sqrt{5}}-\sqrt{62\sqrt{5}}\)
b)\(\sqrt{24-8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\)
c) \(\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}\)
d)\(\sqrt{41+12\sqrt{5}}-\sqrt{46-6\sqrt{ }5}\)
e)\(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)
f)\(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)
g) \(\sqrt{43+24\sqrt{3}}-\sqrt{49-8\sqrt{3}}\)
