a) \(\sqrt{16}+\sqrt{1}-3\sqrt{9}=4+1-3.3=-4\)
b) \(\sqrt{\dfrac{4}{9}}-\sqrt{25}+\sqrt{100}=\dfrac{2}{3}-5+10=\dfrac{17}{3}\)
c) \(2\sqrt{169}+3\sqrt{196}-2\sqrt{289}\)
= \(2.13+3.14-2.17=34\)
Tìm giá trị các biểu thức sau bằng cách biến đổi rút gọn thích hợp :
a) \(\sqrt{\dfrac{25}{81}.\dfrac{16}{49}.\dfrac{196}{9}}\)
b) \(\sqrt{3\dfrac{1}{16}.2\dfrac{14}{25}.2\dfrac{34}{81}}\)
c) \(\dfrac{\sqrt{640}.\sqrt{34,3}}{\sqrt{567}}\)
d) \(\sqrt{21,6}.\sqrt{810}.\sqrt{11^2-5^2}\)
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) \(\dfrac{1}{2}\sqrt{\dfrac{49x}{x+2}}-3\sqrt{\dfrac{x}{4x+8}}-\sqrt{\dfrac{x}{x+2}}-\sqrt{5}=0\)
thực hiện phép tính:
A=\(\sqrt{9}-3\sqrt{\dfrac{50}{9}}+3\sqrt{8}-\sqrt[3]{27}\)
B=\(\sqrt{\left(2-\sqrt{3}\right)^2}+\dfrac{2}{\sqrt{3}-1}-6\sqrt{\dfrac{16}{3}}\)
Thực hiện phép tính:
1)A=\(\left(\dfrac{1}{3-\sqrt{5}}-\dfrac{1}{3+\sqrt{5}}\right)\) . \(\dfrac{5-\sqrt{5}}{\sqrt{5}-1}\)
2)B = \(\dfrac{1}{1 +\sqrt{2}}\) +\(\dfrac{1}{\sqrt{2}+\sqrt{3}}\)+.....+\(\dfrac{1}{\sqrt{99}+\sqrt{100}}\)
3)C = \(\sqrt[3]{7+5\sqrt{2}}\) - \(\sqrt[3]{7-5\sqrt{2}}\)
4) D = \(\sqrt[3]{9+4\sqrt{5}}\)+\(\sqrt[3]{9-4\sqrt{3}}\)
tính
a, \(\sqrt{169}\) - \(\sqrt{225}\)
b \(\dfrac{\sqrt{144}}{9}\)
c \(\sqrt{18}\) \(\div\) \(\sqrt{2}\)
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)\(\sqrt{17-3\sqrt{ }32+\sqrt{ }17+\sqrt{ }32}\)
Bài 1: Cho A = \(\dfrac{1}{2\sqrt{1}+1\sqrt{2}}+\dfrac{1}{3\sqrt{2}+2\sqrt{3}}+\dfrac{1}{4\sqrt{3}+3\sqrt{4}}+...+\dfrac{1}{100\sqrt{99}+99\sqrt{100}}\)
So sánh A với 1
Bài 2: Tính
A = \(\left(\dfrac{3}{\sqrt{2}+1}+\dfrac{14}{2\sqrt{2}-1}-\dfrac{4}{2-\sqrt{2}}\right).\left(\sqrt{8}+2\right)\)
Bài 3: Tính tổng
S=\(\dfrac{1}{\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{4}}+\dfrac{1}{\sqrt{4}+\sqrt{5}}+...+\dfrac{1}{\sqrt{2018}+\sqrt{2019}}\)
Tính GTBT
a,M=\(\left(3x^3-x^2-1\right)^{2018}\) biết x = \(\dfrac{\sqrt[3]{26+15\sqrt{3}}\left(2-\sqrt[]{3}\right)}{\sqrt[3]{9+\sqrt{80}}+\sqrt[3]{9-\sqrt{80}}}\)
b,\(x^3+ax+b\) biết x=\(\sqrt[3]{\dfrac{-b}{2}+\sqrt{\dfrac{b^2}{4}+\dfrac{a^3}{27}}}+\sqrt[3]{\dfrac{-b}{2}-\sqrt{\dfrac{b^2}{4}+\dfrac{a^3}{27}}}\)
Rút gọn
A=\(\dfrac{1}{\sqrt{1}-\sqrt{2}}-\dfrac{1}{\sqrt{2}-\sqrt{3}}+\dfrac{1}{\sqrt{3}-\sqrt{4}}-...-\dfrac{1}{\sqrt{24}-\sqrt{25}}\)
B=\(\dfrac{5}{4+\sqrt{11}}+\dfrac{11-3\sqrt{11}}{\sqrt{11}-3}-\dfrac{4}{\sqrt{5}-1}+\sqrt{\left(\sqrt{5}-2\right)^2}\)
C=\(\dfrac{\sqrt{x}+1}{x\sqrt[]{x}+x+\sqrt{x}}:\dfrac{1}{x^2-\sqrt{x}}\) (với x>0; x#1)
D=\(\dfrac{\sqrt{x^2-10x+25}}{x-5}\)
