a: \(\sqrt{169}-\sqrt{225}\)
\(=\sqrt{13^2}-\sqrt{15^2}\)
=13-15
=-2
b: \(\dfrac{\sqrt{144}}{9}\)
\(=\dfrac{\sqrt{12^2}}{9}\)
\(=\dfrac{12}{9}=\dfrac{4}{3}\)
c: \(\sqrt{18}:\sqrt{2}=\sqrt{\dfrac{18}{2}}=\sqrt{9}=3\)
Đề bài: Tách:
a) \(\sqrt{16}+\sqrt{1}-3\sqrt{9}\)
b)\(\sqrt{\dfrac{4}{9}}-\sqrt{25}+\sqrt{100}\)
c) \(2\sqrt{169}+3\sqrt{196}-2\sqrt{289}\)
1) Giải phương trình: a) \(5\sqrt{\dfrac{9x-27}{25}}-7\sqrt{\dfrac{4x-12}{9}}-7\sqrt{x^2-9}+18\sqrt{\dfrac{9x^2-81}{91}}=0\) b) \(\sqrt{x}+\sqrt{y-1}+\sqrt{z-2}=\dfrac{1}{2}\left(x+y+z\right)\)
a) \(\dfrac{5-2\sqrt{ }5}{\sqrt{ }5-2}-\dfrac{11}{4+\sqrt{ }5} \)
b)\(\sqrt{9+4\sqrt{ }5-\sqrt{ }6-2\sqrt{ }5}\)
c)\(\sqrt{17-3\sqrt{ }32+\sqrt{ }17+\sqrt{ }32}\)
Giải PT:
a) \(\dfrac{1}{2}\sqrt{x-1}-\dfrac{3}{2}\sqrt{9x-9}+24\sqrt{\dfrac{x-1}{64}}=-17\)
b) \(\sqrt{18x-9}-0,5\sqrt{2x-1}+\dfrac{1}{2}\sqrt{25\left(2x-1\right)}+\sqrt{49\left(2x-1\right)}=24\)
c) \(\sqrt{36x-72}-15\sqrt{\dfrac{x-2}{25}}=4\left(5+\sqrt{x-2}\right)\)
d) \(\sqrt{\dfrac{1}{3x+2}}-\dfrac{1}{2}\sqrt{\dfrac{9}{3x+2}}+\sqrt{\dfrac{16}{3x+2}}-5\sqrt{\dfrac{1}{12x+8}}=1\)
e) \(\dfrac{1}{2}\sqrt{\dfrac{49x}{x+2}}-3\sqrt{\dfrac{x}{4x+8}}-\sqrt{\dfrac{x}{x+2}}-\sqrt{5}=0\)
tính
a, \(\sqrt{\left(3-\sqrt{5}\right)^2}\) - \(\sqrt{5}\)
b \(\sqrt{\left(4-2\sqrt{3}\right)^2}\)
thực hiện phép tính:
A=\(\sqrt{9}-3\sqrt{\dfrac{50}{9}}+3\sqrt{8}-\sqrt[3]{27}\)
B=\(\sqrt{\left(2-\sqrt{3}\right)^2}+\dfrac{2}{\sqrt{3}-1}-6\sqrt{\dfrac{16}{3}}\)
Bài 1 :tính giá trị của biểu thức
a) \(\left(\sqrt{5}+\sqrt{2}\right)\left(3\sqrt{2}-1\right)\)
b) \(3\sqrt{50}-2\sqrt{75}-4\dfrac{\sqrt{54}}{\sqrt{3}}-3\sqrt{\dfrac{1}{3}}\)
c) \(\sqrt{\left(\sqrt{3}-3\right)^2}+\sqrt{4+2\sqrt{3}}\)
d) \(\sqrt{48-2\sqrt{135}}-\sqrt{45}+\sqrt{18}\)
e)\(\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}+\dfrac{6}{2-\sqrt{10}}-\dfrac{20}{\sqrt{10}}\)
Bài 2 :Tính:
a) \(3\sqrt{2x}-5\sqrt{8x}+7\sqrt{18x}\)
b) \(\left(2\sqrt{3}+4\right)\left(\sqrt{3}-2\right)\)
c) \(\sqrt{3+2\sqrt{2}}+\sqrt{\left(\sqrt{2}-2\right)^2}\)
d)\(\sqrt{4-\sqrt{15}}-\sqrt{4+\sqrt{15}}+\sqrt{6}\)
e)\(\left(\dfrac{5-\sqrt{5}}{\sqrt{5}}-2\right)\left(\dfrac{4}{1+\sqrt{5}}+4\right)\)
f) \(\dfrac{1}{5}\sqrt{50}-2\sqrt{96}-\dfrac{\sqrt{30}}{\sqrt{15}}+12\sqrt{\dfrac{1}{6}}\)
giải pt:
\(\dfrac{1}{2}\sqrt{x-2}-4\sqrt{\dfrac{4x-8}{9}}+\sqrt{9x+18}-5=0\)
Tìm x thỏa mãn:
\(\left(\sqrt{x}+1\right)\dfrac{\sqrt{x}+2}{\sqrt{x}+1}-\sqrt{x}-4\sqrt{x-1}+26=-6x+10\sqrt{5x}\)
giải phương trình
a, \(\sqrt{4x-20}+3\sqrt{\dfrac{x-5}{9}}-\dfrac{1}{3}\sqrt{9x-45}=4\)
b, \(2x-x^2+\sqrt{6x^2-12x+7}=0\)
c, \(\dfrac{9x-7}{\sqrt{7x+5}}=\sqrt{7x+5}\)
