BÀI 1 : THỰC HIỆN PHÉP TÍNH
a, \(\left(1+\sqrt{3}-\sqrt[2]{2}\right)\times\left(1+\sqrt{3}+\sqrt[2]{2}\right)\)
b, \(\left(\dfrac{3}{2}\times\sqrt{6}+2\times\sqrt{\dfrac{2}{3}}-4\times\sqrt{\dfrac{3}{2}}\right)\times\left(3\times\sqrt{\dfrac{2}{3}}-\sqrt{12}-\sqrt{6}\right)\)
BÀI 2 : rút gọn
B = \(\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-2}}\)
bài 1 : rút gọn các biểu thức sau .
a, \(\sqrt{4\left(a-3\right)^2}+2\sqrt{a^2+4a+4}\left(a< -2\right)\)
b, \(\sqrt{\dfrac{\left(x-2\right)^2}{\left(3-2\right)^2}}+\dfrac{x^2-1}{x-3}\left(x< 3\right)\)
c, \(4x-\sqrt{8}+\dfrac{\sqrt{x^3+2x^2}}{\sqrt{x+2}}\)
bài 2 thực hiện phép tính :\
a, \(\sqrt{8-\sqrt[2]{7}}\times\sqrt{8+\sqrt[2]{7}}\)
b, \(\sqrt{4+\sqrt{8}+}+\sqrt{2}+\sqrt{2+\sqrt{2}}\times\sqrt{2-\sqrt{2+2}}\)
c, \(\left(4+\sqrt{15}\right)\times\sqrt{10}-\sqrt{6}\times\sqrt{4-\sqrt{15}}\)
d, \(\left(2+\sqrt{3}\right)^2-\left(2-\sqrt{3}\right)\times\left(2+\sqrt{3}\right)\)
bài 1 ; thực hiện phép tính
a, \(\left(\sqrt{12}+\sqrt{75}+\sqrt{27}\right):\sqrt{15}\)
b, \(\sqrt{252}-\sqrt{700}+\sqrt{1008}-\sqrt{448}\)
c, \(\sqrt{27^2-23^2}+\sqrt{37^2-35^2}\)
d,\(\left(\sqrt{\dfrac{1}{7}}+\sqrt{\dfrac{16}{7}}+\sqrt{\dfrac{9}{7}}\right):\sqrt{7}\)
bài 2 : rút gọn
a, \(A=\dfrac{2}{x^2-y^2}\times\sqrt{\dfrac{3x^2+6xy+3y^2}{4}}\)
b, \(B=\dfrac{1}{2a-1}\times\sqrt{5a^4\left(1-4a+4a^2\right)}\)
A)\(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}+\sqrt{2}\right)\)
B)\(\left(\sqrt{2}+1^{ }\right)^3-\left(\sqrt{2}-1\right)^3\) C)\(\dfrac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\) D)\(\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}}+\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}}\) E)\(\dfrac{\sqrt{3-\sqrt{5}}.\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\) F)\(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
rút gọn hoạc tính giá trị các biểu thức sau
1)1+\(\sqrt{\dfrac{\left(x-1\right)^2}{x-1}}\)
2)\(\sqrt{\left(x-2\right)^2}+\dfrac{x-2}{\sqrt{\left(x-2\right)^2}}\)
3)\(\sqrt{m}-\sqrt{m-2\sqrt{m}+1}\)
B2 : Tính :
a, \(\left(\sqrt{x}-3\right)\)\(.\left(\sqrt{x}+2\right)\)
b, \(\left(\sqrt{x}-\sqrt{y}\right).\)\(\left(\sqrt{x}+\sqrt{y}\right)\)
c, \(\left(\sqrt{\dfrac{25}{3}}-\sqrt{\dfrac{49}{3}}+\sqrt{3}\right)\)\(.\sqrt{3}\)
d,\(\left(1+\sqrt{3}-\sqrt{5}\right)\)\(.\left(1+\sqrt{3}+\sqrt{5}\right)\)
\(\left(\dfrac{1}{3}\sqrt{\dfrac{1}{2}}-\dfrac{2}{3}\sqrt{\dfrac{3}{2}}+\dfrac{2}{7}\sqrt{\dfrac{1}{6}}\right):\left(\dfrac{2}{7}\sqrt{\dfrac{1}{8}}\right)\)
Rút gọn:
A = \(\sqrt{2}\left(\sqrt{8}-\sqrt{32}-2\sqrt{18}\right)\)
B = \(\left(\sqrt{2}-\sqrt{3-\sqrt{5}}\right)\)
C = \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)
D = \(\sqrt{3}-\sqrt{2}-\sqrt{\sqrt{3}+\sqrt{2}}\)
E = \(\left(\sqrt{2}-\sqrt{3}+\sqrt{5}\right)\sqrt{2}+2\sqrt{5}\)
F = \(\left(\sqrt{14}-\sqrt{10}\right)\left(\sqrt{6+\sqrt{35}}\right)\)
G = \(\sqrt{11-4\sqrt{7}}-\sqrt{2}\times\sqrt{8+3\sqrt{7}}\)
b5: giải pt ;
a, \(\sqrt{49\left(1-2x+x^2\right)}-35=0\)
b, \(\sqrt{x^2-9}-5\sqrt{x+3}=0\)
c, \(\dfrac{\sqrt{x}-2}{\sqrt{x}+1}=\dfrac{\sqrt{x}-1}{\sqrt{x}+3}\)
1. Tính
a. \(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
b.\(\sqrt{3-\sqrt{5}}\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\)
c.\(\dfrac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}-\sqrt{3-2\sqrt{2}}\)
