Chứng tỏ: \(\sqrt[3]{20}+\sqrt[3]{2}+\sqrt[3]{25}=3\sqrt[3]{\sqrt[3]{5}-\sqrt[3]{4}}\)
Chứng minh
\(\sqrt{x-3}+\sqrt{y-5}+\sqrt{z-4}=20-\frac{4}{\sqrt{x-3}}-\frac{9}{\sqrt{y-5}}-\frac{25}{\sqrt{z-4}}\)
BÀI 1: RÚT GỌN
1)\(\frac{1}{\sqrt{3}+1}+\frac{1}{\sqrt{3}-1}\)
2)\(\sqrt{7+2\sqrt{10}}+2\sqrt{\frac{1}{5}}-\frac{1}{\sqrt{5}-2}\)
3)\(\frac{3}{\sqrt{3}-1}+\sqrt{\frac{4}{3}}-\sqrt{8+2\sqrt{5}}\)
4)\(3\sqrt{\frac{16x}{81}}+\frac{5}{4}\sqrt{\frac{4x}{25}}-\frac{2}{x}\sqrt{\frac{9a^3}{4}}\)
5)\(\frac{1}{3}\sqrt{3a}-\frac{2}{3}\sqrt{\frac{27a}{4}}+\frac{5}{a}\sqrt{\frac{12a^3}{5}}\)
BÀI 2: GIẢI PHƯƠNG TRÌNH
\(1)\sqrt{5x-1}=\sqrt{2}-1\\ 2)\sqrt{1-2x}=\sqrt{3}-1\\ 3)4\sqrt{x}-2\sqrt{9x}+\sqrt{16x}=20\\ 4)\frac{3}{5}\sqrt{\frac{25x-75}{16}}-\frac{1}{14}\sqrt{49x-147}=20\\ 5)\frac{1}{2}\sqrt{x-2}-4\sqrt{\frac{4x-8}{9}}+\sqrt{9x-18}-5=0\)
BÀI 3: CHO BIỂU THỨC
Q=\(\frac{2}{2+\sqrt{x}}+\frac{1}{2-\sqrt{x}}+\frac{2\sqrt{x}}{x-4}\) ĐKXĐ x ≥ 0, x ≠ 4
a) Rút gọn biểu thức Q
b) Tính Q thì x = 81
c) Tìm x để Q = \(\frac{6}{5}\)
d) Tìm x để nguyên đó Q nguyên
Tính giá trị của biểu thức sau:
\(a,^3\sqrt{26+15\sqrt{3}}-^3\sqrt{26-15\sqrt{3}}\)
\(b,^3\sqrt{9+4\sqrt{5}}+^3\sqrt{9-4\sqrt{5}}\)
\(c,^3\sqrt{20+14\sqrt{2}}+^3\sqrt{20-14\sqrt{2}}\)
tinh
a. \(\sqrt{5}-\sqrt{48}+5\sqrt{27}-\sqrt{45}\)
b.\(\left(\sqrt{5}+\sqrt{2}\right)\left(3\sqrt{2}-1\right)\)
c.\(3\sqrt{50}-2\sqrt{75}-4\frac{\sqrt{54}}{\sqrt{3}}-3\sqrt{\frac{1}{3}}\)
d.\(\sqrt{\left(\sqrt{3}-3\right)^2}+\sqrt{4-2\sqrt{3}}\)
e.\(\frac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}+\frac{6}{2-\sqrt{10}}-\frac{20}{\sqrt{10}}\)
f.\(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}+1}{\sqrt{5}-1}\)
3. a.\(\sqrt{\left(4-\sqrt{17}\right)^2}\)
b.\(\frac{2\sqrt{3}}{2}\)
c \(\frac{\sqrt{6}+\sqrt{14}}{\text{2√3+√28}}\)
d.\(\frac{x+1}{\sqrt{x^2-1}}\)
e.\(\frac{x^2-5}{x+\sqrt{5}}\)
f.\(\frac{2}{2-\sqrt{3}}\)
g.\(\frac{\sqrt{2}+1}{\sqrt{2}-1}\)
f.\(\frac{x\sqrt{x}-1}{\sqrt{x}-1}\)
i.\(\frac{3}{\sqrt{20}}+\frac{1}{\sqrt{60}}-2\sqrt{\frac{1}{15}}\)
k.\(\frac{3}{\sqrt{5}-\sqrt{2}}+\frac{4}{\sqrt{6}+\sqrt{2}}\)
i.(\(\frac{1}{\sqrt{5}-\sqrt{3}}+\frac{1}{\sqrt{5}+\sqrt{3}}\))\(\sqrt{5}\)
h.\(\left(\sqrt{20}-\sqrt{45}+\sqrt{5}\right)\sqrt{5}\)
l.\(\left(5\sqrt{3}+3\sqrt{5}\right):\sqrt{15}\)
m.\(\frac{1}{3}\sqrt{48}+3\sqrt{75}-\sqrt{27}-10\sqrt{\frac{4}{3}}\)
n.\(\left(5\sqrt{\frac{1}{5}}+\frac{1}{2}\sqrt{20}-\frac{5}{4}\sqrt{\frac{4}{5}+\sqrt{5}}\right):2\sqrt{5}\)
d\(\left(2+\sqrt{5}\right)^2-\left(2+\sqrt{5}\right)^2\)
Chứng tỏ :\(\sqrt[3]{20}+\sqrt[3]{2}-\sqrt[3]{2}=3\sqrt{\sqrt[3]{5}-\sqrt[3]{4}}\)
Thực hiện phép tính:
a) \(\left(\frac{1}{7-4\sqrt{3}}+\frac{3}{7+4\sqrt{3}}\right)\left(7+2\sqrt{3}\right)\)
b)\(\left(\frac{3\sqrt{5}-\sqrt{15}}{\sqrt{27}-3}+\frac{2\sqrt{5}}{\sqrt{3}}\right).4\sqrt{15}\)
c)\(\sqrt{5-2\sqrt{6-25-\sqrt{96}}}\)
d)\(\sqrt{23-2\sqrt{112}}+\sqrt{23+2\sqrt{112}}\)
giúp mk tính
a,\(\sqrt{5}-\sqrt{48}+5\sqrt{27}-\sqrt{45}\)
b,(\(\sqrt{5}+\sqrt{2}\)) (\(3\sqrt{2}-1\))
c,\(3\sqrt{50}-2\sqrt{75}-4\dfrac{\sqrt{54}}{\sqrt{3}}-3\sqrt{\dfrac{1}{3}}\)
d, \(\sqrt{\left(\sqrt{3}-3\right)^2}+\sqrt{4-2\sqrt{3}}\)
e, \(\sqrt{48-2\sqrt{135}}-\sqrt{45}+\sqrt{18}\)
f, \(\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}+\dfrac{6}{2-\sqrt{10}}-\dfrac{20}{\sqrt{10}}\)
bài 2
a, \(\sqrt{9-4\sqrt{5}}\)
b,\(2\sqrt{3}+\sqrt{48}-\sqrt{75}-\sqrt{243}\)
c\(\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\)
d, \(\sqrt{3+2\sqrt{2}}-\sqrt{6-4\sqrt{2}}\)
e,\(\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}\)+\(\dfrac{\sqrt{3}+\sqrt{5}}{\sqrt{5}-\sqrt{3}}-\dfrac{\sqrt{5}+1}{\sqrt{5}-1}\)
f, \(\sqrt{5\sqrt{3+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)