\(A=\dfrac{2\sqrt{a}\left(a+1\right)-3\left(a+1\right)}{2\sqrt{a}-3}=a+1\)
\(B=\dfrac{2a\left(a-1\right)}{\sqrt{a}\left(a-1\right)}=2\sqrt{a}\)
\(A-B=a+1-2\sqrt{a}=\left(\sqrt{a}-1\right)^2>=0\)
=>A>=B
Rút gọn các biểu thức sau:
a. \(\sqrt{\dfrac{2a}{3}}.\sqrt{\dfrac{3a}{8}}\) với \(a\ge0;\)
b. \(\sqrt{13a}.\sqrt{\dfrac{52}{a}}\) với a > 0;
c. \(\sqrt{5a}.\sqrt{45a}-3a\) với \(a\ge0;\)
d. \(\left(3-a\right)^2-\sqrt{0,2}.\sqrt{180a^2}.\)
Rút gọn:
a. \(\sqrt{2a}\) \(\times\) \(\sqrt{18a}\) (a \(\ge\)0)
b. \(\sqrt{3a\times27ab^2}\)
c. 2y2 \(\times\) \(\sqrt{\dfrac{x^4}{4y^2}}\) (y < 0)
d. \(\dfrac{y}{x}\) \(\times\) \(\sqrt{\dfrac{x^2}{y^4}}\) (x > 0 ; y \(\ne\)0)
e. \(\sqrt{\dfrac{9a^2}{16}}\)
f. \(\sqrt{10.16a^2}\) (a < 0)
g. \(\sqrt{a^4}\left(3-a\right)^2\) (a \(\ge\) 3)
h. \(\sqrt{\dfrac{2a^2b^4}{98}}\)
Rút gọn :
a) \(\dfrac{3\sqrt{2-6}}{\sqrt{2-1}}\)
b) \(\dfrac{3\sqrt{5}+5\sqrt{3}}{\sqrt{3}+\sqrt{5}}\)
c) \(\dfrac{x-y}{\sqrt{x}-\sqrt{y}}\)
Rút gọn các biểu thức sau :
a,\(\dfrac{\sqrt{6}+\sqrt{10}}{\sqrt{21}+\sqrt{35}}\)
b,\(\dfrac{\sqrt{405}+3\sqrt{27}}{3\sqrt{3}+\sqrt{45}}\)
c,\(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{4}-\sqrt{6}-\sqrt{9}-\sqrt{12}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
d, D=\(\dfrac{2}{x^2-y^2}\cdot\sqrt{\dfrac{9\left(x^2+2xy+y^2\right)}{4}}\) \(\left(vớix\ne y,x\ne-y\right)\)
Rút gọn:
a)\(\dfrac{\sqrt{a}+a\sqrt{b}-\sqrt{b}-b\sqrt{a}}{ab-1}\)
b) \(\dfrac{2\sqrt{15}-2\sqrt{10}+\sqrt{6}-3}{2\sqrt{5}-2\sqrt{10}-\sqrt{3}+\sqrt{6}}\)
Rút gọn :
a) \(\dfrac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}\)
b) \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
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, \(B=\dfrac{1}{2a-1}\times\sqrt{5a^4\left(1-4a+4a^2\right)}\)
bài 1: rút gọn các biểu thức.
a) \(\dfrac{x\sqrt{x}+y\sqrt{y}}{\sqrt{x}+\sqrt{y}}-(\sqrt{x}-\sqrt{y})^2\)
b) \(\sqrt{\dfrac{x-2\sqrt{x}+1}{x+2\sqrt{x}+1}}(x\ge0)\)
c) \(\dfrac{x-1}{\sqrt{y}-1}\sqrt{\dfrac{(y-2\sqrt{y}+1)^2}{(x-1)^4}}(x\ne1,y\ne1,y>0)\)
bài 2:rút gọn và tính.
a) \(\sqrt{\dfrac{\sqrt{a}-1}{\sqrt{b}+1}:}\sqrt{\dfrac{\sqrt{b}-1}{\sqrt{a}+1}với}a=7,25;b=3,25\)
b) \(\sqrt{15a^2-8a\sqrt{15}+16}vớia=\sqrt{\dfrac{3}{5}}+\sqrt{\dfrac{5}{3}}\)
c) \(\sqrt{10a^2-4a\sqrt{10}+4}vớia=\sqrt{\dfrac{2}{5}}+\sqrt{\dfrac{5}{2}}\)
d) \(\sqrt{a^2+2\sqrt{a^2-1}}-\sqrt{a^2-2\sqrt{a^2-1}}(a=\sqrt{5})\)
bài 3: rút gọn các biểu thức.
a) \(\sqrt{9(x-5)^2}(x\ge5)\)
b) \(\sqrt{x^2.(x-2)^2}(x< 0)\)
c)\(\dfrac{\sqrt{108x^3}}{\sqrt{12x}}(x>0)\)
d)\(\dfrac{\sqrt{13x^4y^6}}{\sqrt{208x^6y^6}}(x< 0:y\ne0)\)
ai giúp mik vs ạ, cảm ơn !
rút gọn biểu thức
a,\(\sqrt{36\left(6-2\right)^2}\) với b <2
b,\(\sqrt{b^2\left(b-1\right)^2}\) với b >0
c, \(\sqrt{a^2\left(a+1\right)^2}\) với a >0
d, \(\sqrt{\left(2a-1\right)^2}-4a\) với a < \(\dfrac{1}{2}\)
