Rút gọn các biểu thức:
a)\(\frac{\sqrt{63y^3}}{\sqrt{7y}}\) (y>0).
b)\(\frac{\sqrt{48x^3}}{\sqrt{3x^5}}\) (x>0).
c)\(\frac{\sqrt{45mn^2}}{\sqrt{20m}}\) (m>0 và n>0).
d)\(\frac{\sqrt{16a^4b^6}}{\sqrt{128a^6b^6}}\) (a<0 và b khác 0).
*Liên hệ giữa phép chia và phép khai phương :
Rút gọn các biểu thức :
a,\(\frac{\sqrt{63y^3}}{\sqrt{7y}}\) (y>0)
b,\(\frac{\sqrt{48x^3}}{\sqrt{3x^5}}\) (x>0)
c,\(\frac{\sqrt{45mn^2}}{\sqrt{20m}}\) (m>0 và n>0)
d,\(\frac{\sqrt{16a^4b^6}}{\sqrt{128a^6b^6}}\) (a<0 và b khác 0)
e,\(\sqrt{\frac{x-2\sqrt{x}+1}{x+2\sqrt{x}+1}}\) (x\(\ge\) 0)
f, \(\frac{x-1}{\sqrt{y}-1}\sqrt{\frac{\left(y-2\sqrt{y}+1\right)}{\left(x-1\right)^4}}\) (x\(\ne\)1 , y\(\ne\)1 và y\(\ge\)0)
Rút gọn các biểu thức
a) \(\dfrac{\sqrt{63y^3}}{\sqrt{7y}};\left(y>0\right)\)
b) \(\dfrac{\sqrt{48x^3}}{\sqrt{3x^5}};\left(x>0\right)\)
c) \(\dfrac{\sqrt{45mn2}}{\sqrt{20m}};\left(m>0;n>0\right)\)
d) \(\dfrac{\sqrt{16a^4b^6}}{\sqrt{128a^6b^6}};\left(a< 0;b\ne0\right)\)
a. \(\sqrt{\dfrac{63y^3}{7y}}\)=\(\sqrt{9y^2}\)=3y
b.\(\sqrt{\dfrac{48x^3}{3x^5}}\)=\(\sqrt{16\cdot\dfrac{1}{X^2}}\)= \(\sqrt{16}\cdot\sqrt{\dfrac{1}{X^2}}\)=\(4\cdot\dfrac{1}{X}=\dfrac{4}{X}\)
c.\(\sqrt{\dfrac{45mn^2}{20m}}=\sqrt{\dfrac{9n^2}{4}}=\dfrac{\sqrt{9n^2}}{\sqrt{4}}=\dfrac{3n}{2}\)
d. \(\sqrt{\dfrac{16a^4b^6}{128a^6b^6}}=\sqrt{\dfrac{1}{8a^2}}=\dfrac{1}{2\sqrt{2}a}\)
a) \(\dfrac{\sqrt{63y^3}}{\sqrt{7y}}=\sqrt{\dfrac{63y^3}{7y}}=\sqrt{9y^2}=3y\)
b) \(\dfrac{\sqrt{48x^3}}{\sqrt{3x^5}}=\sqrt{\dfrac{48x^3}{3x^5}}=\sqrt{\dfrac{16}{x^2}}=\dfrac{4}{x}\)
c) \(\dfrac{\sqrt{45mn^2}}{\sqrt{20m}}=\sqrt{\dfrac{45mn^2}{20m}}=\sqrt{\dfrac{9n^2}{4}}=\dfrac{3n}{2}\)
d) \(\dfrac{\sqrt{16a^4b^6}}{\sqrt{128a^6b^6}}=\sqrt{\dfrac{16a^4b^6}{128a^6b^6}}=\sqrt{\dfrac{1}{8a^2}}=\dfrac{1}{2\left|a\right|\sqrt{2}}=\dfrac{-1}{2a\sqrt{2}}\)
rút gọn:
\(a,\frac{\sqrt{4mn^2}}{\sqrt{20m}}\left(m>0,n>0\right)\)
\(b,\frac{\sqrt{16a^4b^6}}{\sqrt{12a^6b^6}}\left(a< 0,b\ne0\right)\)
\(c,\frac{y-\sqrt{xy}}{x-\sqrt{xy}}\)với\(xy>0,y\ne1\)
\(d,\frac{x\sqrt{x}-y\sqrt{y}}{\sqrt{x}-\sqrt{y}}\)với \(x>0,y>0,y\ne1\)
\(e,\sqrt{\frac{x-2\sqrt{x}+1}{x+2\sqrt{x}+1}}\)với \(x>0\)
a) \(\frac{\sqrt{4mn^2}}{\sqrt{20m}}=\sqrt{\frac{4mn^2}{20m}}=\sqrt{\frac{n^2}{5}}=\frac{n}{\sqrt{5}}\)
b) \(\frac{\sqrt{16a^4b^6}}{\sqrt{12a^6b^6}}=\sqrt{\frac{16a^4b^6}{12a^6b^6}}=\sqrt{\frac{4}{3a^2}}=\frac{2}{\sqrt{3}.\left|a\right|}=-\frac{2}{a\sqrt{3}}\)
d) \(\frac{x\sqrt{x}-y\sqrt{y}}{\sqrt{x}-\sqrt{y}}=\frac{\left(\sqrt{x}-\sqrt{y}\right)\left(x+\sqrt{xy}+y\right)}{\sqrt{x}-\sqrt{y}}=x+\sqrt{xy}+y\)
e) \(\sqrt{\frac{x-2\sqrt{x}+1}{x+2\sqrt{x}+1}}=\sqrt{\frac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}+1\right)^2}}=\frac{\left|\sqrt{x}-1\right|}{\sqrt{x}+1}\)
Rút gọn biểu thức:
\(\sqrt{\frac{2a}{3}}.\sqrt{\frac{3a}{8}}vớia\ge0\)\(\sqrt{5a}.\sqrt{45a}-3avớia\ge0\)\(4\sqrt{16a^6}-6a^3\rightarrow kq2TH\)\(\left(3-a\right)^2-\sqrt{0,2}.\sqrt{180a^4}\)\(\sqrt{\frac{27.\left(a-3\right)^2}{48}}vớia< 3\)\(\frac{\sqrt{63y^3}}{\sqrt{7y}}vớiy>0\)\(\frac{\sqrt{16a^4b^6}}{\sqrt{128a^6b^2}}vớia< 0,b\ne0\)\(\frac{a-b}{\sqrt{a}-\sqrt{b}}-\frac{\sqrt{a^3}+\sqrt{b^3}}{a-b}\left(a\ge0;b\ge0;a\ne b\right)\)\(\frac{2a+\sqrt{ab}-3b}{2a-5\sqrt{ab}+3b}\left(a,b\ge0;4a\ne9b\right)\)Rút gọn biểu thức
a)\(\frac{\sqrt{2x^3}}{\sqrt{8x}}\)(x>0)
b)(3−√5)(3+√5)
c)\(\sqrt{\frac{3x^2y^4}{27}}\)(x<0,x=0)
e)\(\frac{y}{x^2}\sqrt{\frac{36x^4}{y^2}}\)(y<0)
f)\(\frac{\sqrt{99999999}}{\sqrt{11111111}}\)
MK CẦN GẤP CÁC BẠN GIÚP MÌNH NHÉ!!! PLEASE
a) \(\frac{\sqrt{2x^3}}{\sqrt{8x}}=\sqrt{\frac{2x^3}{8x}}=\frac{1}{2}x\)
b) \(\left(3-\sqrt{5}\right)\left(x+\sqrt{5}\right)=3^2-\left(\sqrt{5}\right)^2=9-5=4\)
c) \(\sqrt{\frac{3x^2y^4}{27}}=0\)
\(y\ne0\)
Thì \(\sqrt{\frac{3x^2y^4}{27}}=\frac{1}{3}xy^2\)
e) \(\frac{y}{x^2}\sqrt{\frac{36x^4}{y^2}}=\frac{y}{x^2}.\frac{6x^2}{\left|y\right|}=\frac{6y}{\left|y\right|}\)
Vì y < 0 nên \(\left|y\right|=-y\)
Vậy \(\frac{6y}{\left|y\right|}=\frac{6y}{-y}=-6\)
f) \(\frac{\sqrt{99999999}}{\sqrt{11111111}}=\sqrt{\frac{99999999}{11111111}}=\sqrt{9}=3\)
Rút gọn biểu thức sau
a/ A=\(\frac{x\sqrt{y}-y\sqrt{x}}{\sqrt{xy}}+\frac{x-y}{\sqrt{x}-\sqrt{y}}\)Với x>0 ; y>0 ;x#y
b/ B=\(\frac{3}{2+\sqrt{3}}+\frac{13}{4-\sqrt{3}}+\frac{6}{\sqrt{3}}\)
c/ C=\(\frac{\sqrt{4-2\sqrt{3}}}{\sqrt{6}-\sqrt{2}}\)
d/ D=\(\left(3\sqrt{2}+\sqrt{6}\right)\sqrt{6-3\sqrt{3}}\)
baif1: rút gọn biểu thức:
a)\(\frac{\sqrt{2x^3}}{\sqrt{8x}}\) (x>0)
b)\(\left(3-\sqrt{5}\right)\)\(\left(3+\sqrt{5}\right)\)
c) \(\sqrt{\frac{3x^2y^4}{27}}\)(x<0,x=0)
e)\(\frac{y}{x^2}\)\(\sqrt{\frac{36x^4}{y^2}}\) (y<0)
f)\(\frac{\sqrt{99999999}}{\sqrt{11111111}}\)
Rút gọn biêu thức A = \(\frac{\sqrt{63y^3}}{\sqrt{7y}}\left(y>0\right)\)
\(A=\sqrt{\frac{63y^3}{7y}}=\sqrt{9y^2}=\sqrt{\left(3y\right)^2}=\left|3y\right|=3y\)( y > 0)
\(\frac{\sqrt{48x^3}}{\sqrt{3x^5}}\)(x>0) Rút gọn
\(\frac{\sqrt{48x^3}}{\sqrt{3x^5}}=\sqrt{\frac{48x^3}{3x^5}}=\sqrt{\frac{16}{x^2}}=\frac{4}{x}\)