\(\sqrt[]{9-4\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)
\(=\sqrt{(2-\sqrt{5})^2}-\sqrt{\left(1-\sqrt{5}\right)^2}\)
\(=\left|2-\sqrt{5}\right|-\left|1-\sqrt{5}\right|\)
\(=\sqrt{5}-2-\left(\sqrt{5}-1\right)=\sqrt{5}-2-\sqrt{5}+1\)
\(=-1\)
Thực hiện phép tính (rút gọn biểu thức)
a) \(\sqrt{9+4\sqrt{5}}\) - \(\sqrt{9-4\sqrt{5}}\)
b) \(\sqrt{12-6\sqrt{3}}\) + \(\sqrt{12+6\sqrt{3}}\)
c) \(\sqrt{6\sqrt{2}+11}\) - \(\sqrt{11-6\sqrt{2}}\)
tính ;\(\sqrt{2-\sqrt[3]{3+\sqrt[4]{4-\sqrt[5]{5+\sqrt[6]{6-\sqrt[7]{7+\sqrt[8]{8-\sqrt[9]{9}}}}}}}}\)
Bài 3: Thực hiện các phép tính sau:
a) \(\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\)
b) \(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)
c) \(\sqrt{6-4\sqrt{2}}+\)\(\sqrt{22-12\sqrt{2}}\)
hộ mk với
tính
a/\(\frac{2}{\sqrt{2}-1}-\frac{2}{\sqrt{2}+1}\)
b/\(\sqrt{6+4\sqrt{2}}+\sqrt{6-4\sqrt{2}}\)
c/\(\sqrt{9+4\sqrt{5}}+\sqrt{9-4\sqrt{5}}\)
d/\(\sqrt{3-\sqrt{5}}\cdot(\sqrt{10}-\sqrt{2}).(3+\sqrt{5})\)
11. P=\(\left(\dfrac{\sqrt{x}+2}{\sqrt{x}-2}-\dfrac{\sqrt{x}-2}{\sqrt{x}+2}-\dfrac{4x}{4-x}\right);\dfrac{x+5\sqrt{x}+6}{x-4}\)
a.rút gọn
b. tính giá trị P khi x=\(\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)
c. tìm x để P=2
Tính
\(D=\sqrt{6+2\sqrt{8\sqrt{2}-9}}-\sqrt{7-\sqrt{2}}.\)
\(B=\sqrt{29+6\sqrt{6}}-\sqrt{32-6\sqrt{15}}\)
\(A=\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
Tính:
a.\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
b.\(\sqrt{13+\sqrt{30\sqrt{2+\sqrt{9+4\sqrt{2}}}}}\)
c.\(\frac{\sqrt{9-6\sqrt{2}}-\sqrt{6}}{\sqrt{3}}\)
MÌNH CẦN LUÔN Ạ
Rút gọn biểu thức:
1(2+\(\sqrt{3}\))(7-4\(\sqrt{3}\))
2)\(\left(\sqrt{5-2\sqrt{6}}+\sqrt{2}\right)\sqrt{3}\)
3)\(\sqrt{4+2\sqrt{3}}-\sqrt{5-2\sqrt{6}}+\sqrt{2}\)
4)\(\sqrt{3+2\sqrt{2}}+\sqrt{6-4\sqrt{2}}\)
5)\(2+\sqrt{17-4\sqrt{9+4\sqrt{5}}}\)
Rút gọn:
A=\(\sqrt{6-2\sqrt{5}}-\sqrt{6+2\sqrt{5}}\)
B=\(\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)
C=\(\sqrt{14-6\sqrt{5}-\sqrt{14+6\sqrt{5}}}\)
1) Tính:
\(b,\sqrt{2}.\sqrt{7+3\sqrt{5}}-\dfrac{4}{\sqrt{5-1}}\)
\(c,\sqrt{27}-6\sqrt{\dfrac{1}{3}}+\dfrac{\sqrt{3}-3}{\sqrt{3}}\)
\(d,\dfrac{9-2\sqrt{3}}{3\sqrt{6}-2\sqrt{2}}\)
Giúp mình với, mình cần gấp
