ko biet

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/ \(\frac{3\sqrt{18a^2b^4}}{\sqrt{2a^2b^2}}=\frac{3.3\sqrt{2}.\left|a\right|.\left|b\right|^2}{\sqrt{2}.\left|a\right|.\left|b\right|}=9\left|b\right|\)

\(\dfrac{\sqrt{a}+\sqrt{b}}{2\sqrt{a}-2\sqrt{b}}-\dfrac{\sqrt{a}-\sqrt{b}}{2\sqrt{a}+2\sqrt{b}}-\dfrac{2b}{b-a}\left(a,b>0;a\ne b\right)\\ =\dfrac{\left(\sqrt{a}+\sqrt{b}\right)^2-\left(\sqrt{a}-\sqrt{b}\right)^2+4b}{2\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}\\ =\dfrac{4\sqrt{ab}+4b}{2\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}\\ =\dfrac{4\sqrt{b}\left(\sqrt{a}+\sqrt{b}\right)}{2\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}=\dfrac{2\sqrt{b}}{\sqrt{a}-\sqrt{b}}\)

Tick plz

Ta có: \(\dfrac{\sqrt{a}+\sqrt{b}}{2\sqrt{a}-2\sqrt{b}}-\dfrac{\sqrt{a}-\sqrt{b}}{2\sqrt{a}+2\sqrt{b}}-\dfrac{2b}{b-a}\)

\(=\dfrac{a+2\sqrt{ab}+b-a+2\sqrt{ab}-b+4b}{2\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}\)

\(=\dfrac{4b+4\sqrt{ab}}{2\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}\)

\(=\dfrac{4\sqrt{b}\left(\sqrt{b}+\sqrt{a}\right)}{2\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{b}+\sqrt{a}\right)}\)

\(=\dfrac{2\sqrt{b}}{\sqrt{a}-\sqrt{b}}\)

b. \(=\left(\dfrac{2}{a\left(a+1\right)}-\dfrac{2}{a+1}\right):\dfrac{1-a}{a^2+2a+1}\)

\(=\left(\dfrac{2-2a}{a\left(a+1\right)}\right):\dfrac{1-a}{\left(a+1\right)^1}\)

\(=\dfrac{\left(2-2a\right)\left(a+1\right)^2}{a\left(a+1\right)\left(1-a\right)}\)

\(=\dfrac{2\left(1-a\right)\left(a+1\right)^2}{a\left(a+1\right)\left(1-a\right)}=\dfrac{2\left(a+1\right)}{a}\)

a.\(=\sqrt{2}.\left(\sqrt{25}-\sqrt{9}\right)=\sqrt{2}.\left(5-3\right)=2\sqrt{2}\)

a: \(=5\sqrt{2}-3\sqrt{2}=2\sqrt{2}\)

b: \(=\dfrac{2-2a}{a\left(a+1\right)}\cdot\dfrac{\left(a+1\right)^2}{1-a}=\dfrac{2a+2}{a}\)

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/ \(=\left(1+\frac{\sqrt{a}\left(\sqrt{a}+1\right)}{\sqrt{a}+1}\right)\left(1-\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}\right)\)

\(=\left(1+\sqrt{a}\right)\left(1-\sqrt{a}\right)=1-a\)

a) Ta có: \(A=\dfrac{a^2-1}{3}\cdot\sqrt{\dfrac{9}{\left(1-a\right)^2}}\)

\(=\dfrac{\left(a+1\right)\cdot\left(a-1\right)}{3}\cdot\dfrac{3}{\left|1-a\right|}\)

\(=\dfrac{\left(a+1\right)\left(a-1\right)}{1-a}\)

=-a-1

b) Ta có: \(B=\sqrt{\left(3a-5\right)^2}-2a+4\)

\(=\left|3a-5\right|-2a+4\)

\(=5-3a-2a+4\)

=9-5a

c) Ta có: \(C=4a-3-\sqrt{\left(2a-1\right)^2}\)

\(=4a-3-\left|2a-1\right|\)

\(=4a-3-2a+1\)

\(=2a-2\)

d) Ta có: \(D=\dfrac{a-2}{4}\cdot\sqrt{\dfrac{16a^4}{\left(a-2\right)^2}}\)

\(=\dfrac{a-2}{4}\cdot\dfrac{4a^2}{\left|a-2\right|}\)

\(=\dfrac{a^2\left(a-2\right)}{-\left(a-2\right)}\)

\(=-a^2\)

3a2b4=ab2.3a2b4

3a2.b4=ab2.3|a|.|b2|

3(−a).b2 (Do $a<0$ nên $|a|=-a$ và $b\ne 0$ nên $b^2>0$ $\Rightarrow$  $\left|b^2\right|=b^2$)

$=-\sqrt{3}$.

27(a−3)248=9(a−3)216

9.(a−3)216=3.|a−3|4

3(a−3)4. 

(Do $a>3$ nên $|a-3|=a-3$)

9+12a+4a2b2=32+2.3.2a+(2a)2b2

(3+2a)2b2=|3+2a||b|

3a2b4=ab2.3a2b4

3a2.b4=ab2.3|a|.|b2|

3(−a).b2 (Do $a<0$ nên $|a|=-a$ và $b\ne 0$ nên $b^2>0$ $\Rightarrow$  $\left|b^2\right|=b^2$)

$=-\sqrt{3}$.

27(a−3)248=9(a−3)216

9.(a−3)216=3.|a−3|4

3(a−3)4. 

(Do $a>3$ nên $|a-3|=a-3$)

9+12a+4a2b2=32+2.3.2a+(2a)2b2

(3+2a)2b2=|3+2a||b|

3a2b4=ab2.3a2b4

3a2.b4=ab2.3|a|.|b2|

3(−a).b2 (Do $a<0$ nên $|a|=-a$ và $b\ne 0$ nên $b^2>0$ $\Rightarrow$  $\left|b^2\right|=b^2$)

$=-\sqrt{3}$.

27(a−3)248=9(a−3)216

9.(a−3)216=3.|a−3|4

3(a−3)4. 

(Do $a>3$ nên $|a-3|=a-3$)

9+12a+4a2b2=32+2.3.2a+(2a)2b2

(3+2a)2b2=|3+2a||b|