\(=\sqrt{\dfrac{1}{9}\cdot\dfrac{9}{100}}\cdot64\\ =\sqrt{\dfrac{1}{100}}\cdot64\\ =\sqrt{\left(\dfrac{1}{10}\right)^2}\cdot64\\ =\dfrac{1}{10}\cdot64\\ =\dfrac{32}{5}\)
\(\sqrt{\dfrac{1}{9}}. \sqrt{0,81} .\sqrt{0,09}\)
Tính GT của biểu thức
D = \(\left(6\sqrt{\dfrac{8}{9}}-5\sqrt{\dfrac{32}{45}}+3\sqrt{\dfrac{18}{49}}\right).\sqrt{\dfrac{1}{2}}\)
Thực hiện phép tính:
\(\dfrac{1}{\sqrt{5}+2}-\sqrt{9+4\sqrt{5}}\)
C/m các đẳng thức sau:
a) \(\sqrt{21-6\sqrt{6}}\) + \(\sqrt{9+2\sqrt{18}}\) - \(2\sqrt{6+3\sqrt{3}}\) = 0
b) \(\dfrac{1}{\sqrt{25}+\sqrt{24}}\) + \(\dfrac{1}{\sqrt{24}+\sqrt{23}}\) \(\dfrac{1}{\sqrt{23}+\sqrt{22}}\) +...+ \(\dfrac{1}{\sqrt{2}+\sqrt{1}}\) = 4
c) \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{4}}{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}\) = \(\sqrt{2}\) - 1
Mn giúp mk với !!!
A= \(\dfrac{2\sqrt{a}}{\sqrt{a}+3}\)+\(\dfrac{\sqrt{a}+1}{\sqrt{a}-3}\)+\(\dfrac{3+7\sqrt{a}}{9-a}\)
M = \(\dfrac{x+3}{x-9}+\dfrac{2}{\sqrt{x}+3}-\dfrac{1}{\sqrt{x}-3}\)
a) Rút gọn M
b) Tìm x để M = \(\dfrac{\sqrt{x}+1}{\sqrt{x}+2}\)
tính
\(a,\sqrt{32+10\sqrt{7}}+\sqrt{32-10\sqrt{7}}\)
\(b,\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
\(c,\dfrac{3-\sqrt{x}}{9-x}\) với \(x\ge0,x\ne9\)
\(d,\dfrac{x-5\sqrt{x}+6}{\sqrt{x}-3}\) với \(x\ge0,x\ne9\)
\(e,\dfrac{x-3\sqrt{x}+2}{\sqrt{x}-1}\) với \(x\ge0,x\ne1\)
\(f,\dfrac{x\sqrt{x}+64}{\sqrt{x}+4}\) với \(x\ge0\)
\(g,\dfrac{x\sqrt{x}-y\sqrt{y}}{\sqrt{x}-\sqrt{y}}\) với \(x\ge0,y\ge0,x\ne y\)
\(h,6-2x-\sqrt{9-6x+x^2}\) với \(x< 3\)
\(i,\sqrt{x+2+2\sqrt{x+1}}\) với \(x\ge1\)
Giải các phương trình sau:
a) \(\sqrt{x^2-4+4}=2-x\)
b) \(\sqrt{4x-8}-\dfrac{1}{5}\sqrt{25x-50}=3\sqrt{x-2}-1\)
c) \(\sqrt{x-1}+\sqrt{9x-9}-\sqrt{4x-4}=4\)
d) \(\dfrac{1}{2}\sqrt{x-2}-4\sqrt{\dfrac{4x-8}{9}}+\sqrt{9x-18}-5=0\)
e)\(\sqrt{49-28x+4x^2}-5=0\)
f) \(\sqrt{4x-20}+\sqrt{x-5}-\dfrac{1}{3}\sqrt{9x-45}=4\)
g) x2 - 4x - 2\(\sqrt{2x-5}+5=0\)
h)\(\sqrt{3x-2}=\sqrt{x+1}\)
i) x + y + z + 8 = \(2\sqrt{x-1}+4\sqrt{y-2}+6\sqrt{z-3}\)
k) \(\sqrt{x^2-3x}-\sqrt{x-3}=0\)
l)\(\sqrt{x^2-4}+\sqrt{x-2}=0\)
m) \(4\sqrt{x+1}=x^2-5x+14\)
n) \(\sqrt{x^2-6x+9}-\sqrt{4x^2+4x+1}=0\)
Tính:
a) \(\left(\sqrt{1\dfrac{9}{16}}-\sqrt{\dfrac{9}{16}}\right):5\)
b) \(\left(\sqrt{3}-2\right)^2\left(\sqrt{3}+2\right)^2\)
c) \(\left(11-4\sqrt{3}\right)\left(11+4\sqrt{3}\right)\)
d) \(\left(\sqrt{2}-1\right)^2-\dfrac{3}{2}\sqrt{\left(-2\right)^2}+\dfrac{4\sqrt{2}}{5}+\sqrt{1\dfrac{11}{25}}.\sqrt{2}\)
e) \(\left(1+\sqrt{2021}\right)\sqrt{2022-2\sqrt{2021}}\)
