rút gọn
\(\sqrt{8a^2}.\sqrt{18a^4}\) (a < 0 )
Rút gọn biểu thức :
a) \(\dfrac{a+\sqrt{ab}}{\sqrt{a}+\sqrt{b}}\) ( a > 0 , b > 0 )
b) \(\dfrac{1-8a\sqrt{a}}{1-2\sqrt{a}}\) ( a ≥ 0 , a ≠ \(\dfrac{1}{4}\) )
c) \(\dfrac{1-a}{1+\sqrt{a}}\) ( a ≥ 0 )
d) \(\dfrac{a-3\sqrt{a}}{\sqrt{a}-3}\) ( a ≥ 0 , a ≠ 9 )
a. \(=\dfrac{\sqrt{a}\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{a}+\sqrt{b}}=\sqrt{a}\)
b. \(=\dfrac{1-\left(2\sqrt{a}\right)^3}{1-2\sqrt{a}}=\dfrac{\left(1-2\sqrt{a}\right)\left(1+2\sqrt{a}+4a\right)}{1-2\sqrt{a}}=1+2\sqrt{a}+4a\)
c. \(=\dfrac{1-\left(\sqrt{a}\right)^2}{1+\sqrt{a}}=\dfrac{\left(1+\sqrt{a}\right)\left(1-\sqrt{a}\right)}{1+\sqrt{a}}=1-\sqrt{a}\)
d. \(=\dfrac{\sqrt{a}\left(\sqrt{a}-3\right)}{\sqrt{a}-3}=\sqrt{a}\)
B1: Tính
a) \(.\sqrt{12,1.490}\)
b) \(\sqrt{72.32}\)
B2 : Rút gọn
a) \(\sqrt{48.75a^2}\)
b) \(\sqrt{8a^2}.\sqrt{18a^4}\) với a<0
c) \(\sqrt{a}.\sqrt{\dfrac{9}{a}}\left(a>0\right)\)
d)\(\sqrt{4-2\sqrt{3}}-\sqrt{3}\)
HELP ME !
B1: a) \(\sqrt{12,1.490}=\sqrt{12,1.10.49}=\sqrt{121}.\sqrt{49}=11.7=77\)
b) \(\sqrt{72.32}=\sqrt{36.2.32}=\sqrt{36}.\sqrt{64}=6.8=48\)
B2: a) \(\sqrt{48.75a^2}=\sqrt{3600a^2}=60\left|a\right|\)
b) \(\sqrt{8a^2}.\sqrt{18a^4}=\sqrt{8a^2.18a^4}=\sqrt{144a^6}=-12a^3\)
c) \(\sqrt{a}.\sqrt{\dfrac{9}{a}}=\sqrt{a.\dfrac{9}{a}}=\sqrt{9}=3\)
d) \(\sqrt{4-2\sqrt{3}}-\sqrt{3}=\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{3}=\sqrt{3}-1-\sqrt{3}=-1\)
1 Tính
a) \(\sqrt{0.9\times0.16\times0.4}\)
b) \(\sqrt{0,0016}\)
c)\(\frac{\sqrt{72}}{\sqrt{2}}\)
d) \(\frac{\sqrt{2}}{\sqrt{288}}\)
2 Rút gọn
a) \(\frac{2}{a}.\sqrt{\frac{16a^2}{9}}\left(a< 0\right)\)
b) \(\frac{3}{a-1}.\sqrt{\frac{4a^2-8a+4}{25}}\left(a>1\right)\)
c) \(\frac{\sqrt{243a}}{\sqrt{3a}}\left(a>0\right)\)
d) \(\frac{3\sqrt{18a^2b^4}}{\sqrt{2a^2b^2}}\left(a\ne0,b\ne0\right)\)
1/ a/ \(\sqrt{0,9.0,16.0,4}=\sqrt{\frac{9.16.4}{10000}}=\sqrt{\frac{\left(3.4.2\right)^2}{10^4}}=\frac{24}{1010}=\frac{6}{25}\)
b/ \(\sqrt{0,0016}=\sqrt{\frac{16}{100}}=\frac{4}{10}=\frac{2}{5}\)
c/ \(\frac{\sqrt{72}}{\sqrt{2}}=\frac{\sqrt{2}.\sqrt{36}}{\sqrt{2}}=\sqrt{36}=6\)
d/ \(\frac{\sqrt{2}}{\sqrt{288}}=\frac{\sqrt{2}}{\sqrt{2}.\sqrt{144}}=\frac{1}{\sqrt{144}}=\frac{1}{12}\)
2.
a/ \(\frac{2}{a}.\sqrt{\frac{16a^2}{9}}=\frac{2}{a}.\frac{4\left|a\right|}{3}=-\frac{8a}{3a}=-\frac{8}{3}\) (Vì a<0)
b/ \(\frac{3}{a-1}.\sqrt{\frac{4a^2-8a+4}{25}}=\frac{3}{a-1}.\sqrt{\frac{4\left(a-1\right)^2}{25}}=\frac{3.2\left|a-1\right|}{5.\left(a-1\right)}=\frac{6\left(a-1\right)}{5\left(a-1\right)}=\frac{6}{5}\)
c/ \(\frac{\sqrt{243a}}{\sqrt{3a}}=\frac{9\sqrt{3a}}{\sqrt{3a}}=9\)
d/ \(\frac{3\sqrt{18a^2b^4}}{\sqrt{2a^2b^2}}=\frac{3.3\sqrt{2}.\left|a\right|.\left|b\right|^2}{\sqrt{2}.\left|a\right|.\left|b\right|}=9\left|b\right|\)
Rút gọn biểu thức:
a, \(\frac{2}{a}\sqrt{\frac{16a^2}{9}}\) với a < 0
b, \(\frac{3}{a-1}\sqrt{\frac{4a^2-8a+4}{25}}\) với a > 1
c, \(\frac{3\sqrt{18a^2b^4}}{\sqrt{2a^2b^2}}\) với a ≠ b
d, \(\left(1+\frac{a+\sqrt{a}}{\sqrt{a}+1}\right)\left(1-\frac{a-\sqrt{a}}{\sqrt{a}-1}\right)\) với a ≠ 1, a ≥ 0
a/ \(\frac{2}{a}.\frac{4\left|a\right|}{3}=\frac{-8a}{3a}=-\frac{8}{3}\)
b/ \(\frac{3}{a-1}\sqrt{\frac{4\left(a-1\right)^2}{25}}=\frac{3}{\left(a-1\right)}.\frac{2\left|a-1\right|}{5}=\frac{6\left(a-1\right)}{5\left(a-1\right)}=\frac{6}{5}\)
c/ \(\frac{3\sqrt{9a^2b^4}}{\sqrt{a^2b^2}}=\frac{9.\left|a\right|.b^2}{\left|a\right|\left|b\right|}=9\left|b\right|\)
d/ \(\left(1+\frac{\sqrt{a}\left(\sqrt{a}+1\right)}{\sqrt{a}+1}\right)\left(1-\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}\right)=\left(1+\sqrt{a}\right)\left(1-\sqrt{a}\right)=1-a\)
a/ \(=\frac{2}{a}.\frac{4\left|a\right|}{3}=\frac{2}{a}.\frac{-4a}{3}=\frac{-8}{3}\)
b/ \(=\frac{3}{a-1}.\frac{\left|2a-2\right|}{5}=\frac{3}{a-1}.\frac{2\left(a-1\right)}{5}=\frac{6}{5}\)
c/ \(=\sqrt{\frac{162a^2b^4}{2a^2b^2}}=\sqrt{81b^2}=9\left|b\right|\)
d/ \(=\left(1+\frac{\sqrt{a}\left(\sqrt{a}+1\right)}{\sqrt{a}+1}\right)\left(1-\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}\right)\)
\(=\left(1+\sqrt{a}\right)\left(1-\sqrt{a}\right)=1-a\)
Rút gọn biểu thức:
\(\dfrac{1-8a\sqrt{a}}{1-2\sqrt{a}}\left(a\ge0;a\ne\dfrac{1}{4}\right)\)
`(1-8asqrta)/(1-2sqrta)`
`=(1-(2sqrta)^3)/(1-2sqrta)`
`=((1-2sqrta)(4a+2sqrta+1))/(1-2sqrta)`
`=4a+2sqrta+1`
Rút gọn:
(\(\frac{4\sqrt{a}}{\sqrt{a}+2}\) + \(\frac{8a}{4-a}\)) : (\(\frac{\sqrt{a}-1}{a-2\sqrt{a}}\) - \(\frac{2}{\sqrt{a}}\))
Rút gọn và tính giá trị của biểu thức:
A = \(\sqrt{-8a}\) - \(\sqrt{4a^2-4a+1}\) với a =\(\dfrac{-1}{2}\)
Cho a\(a=\dfrac{13}{\sqrt{19+8\sqrt{3}}}\)
Tính A=\(\dfrac{a^4-6a^3-2a^2+18a+23}{a^2-8a+15}\)
\(a=\dfrac{13}{\sqrt{\left(4+\sqrt{3}\right)^2}}=\dfrac{13}{4+\sqrt{3}}=4-\sqrt{3}\Rightarrow\sqrt{3}=4-a\)
\(\Rightarrow3=16-8a+a^2\Rightarrow a^2-8a+13=0\)
\(A=\dfrac{a^2\left(a^2-8a+13\right)+2a^3-15a^2+18a+23}{a^2-8a+13+2}\)
\(A=\dfrac{2a\left(a^2-8a+13\right)+a^2-8a+13+10}{2}\)
\(A=\dfrac{10}{2}=5\)
rút gọn các biểu thức sau:
a,\(\sqrt{2a}-\sqrt{18a^3}+4\sqrt{\dfrac{a}{2}}\)
a, \(\sqrt{2a}-\sqrt{18a^3}+4\sqrt{\dfrac{a}{2}}\)
=\(\sqrt{2a}-3a\sqrt{2a}+2\sqrt{2a}\)
= (1 - 3a + 2). \(\sqrt{2a}\)
= (3 - 3a).\(\sqrt{2a}\)