Bài 11:
a. $x\sqrt{7}=|x|\sqrt{7}=\sqrt{x^2}.\sqrt{7}=\sqrt{7x^2}$
b.
$x\sqrt{15}=-(-x)\sqrt{15}=-|x|\sqrt{15}=-\sqrt{x^2}.\sqrt{15}$
$=-\sqrt{15x^2}$
c.
$\frac{1}{y}\sqrt{19y}=|\frac{1}{y}|\sqrt{19y}$
$=\sqrt{\frac{1}{y^2}}.\sqrt{19y}=\sqrt{\frac{19}{y}}$
d.
$\frac{1}{3}y\sqrt{\frac{27}{y^2}}=-(\frac{-1}{3}y)\sqrt{\frac{27}{y^2}}$
$=-|\frac{1}{3}y|\sqrt{\frac{27}{y^2}}$
$=-\sqrt{(\frac{1}{3}y)^2}.\sqrt{\frac{27}{y^2}}$
$=-\sqrt{\frac{1}{9}y^2.\frac{27}{y^2}}$
$=-\sqrt{3}$
Bài 12:
a.
$2\sqrt{6}=\sqrt{2^2.6}=\sqrt{24}$
$3\sqrt{3}=\sqrt{3^2.3}=\sqrt{27}$
$\Rightarrow 3\sqrt{3}>2\sqrt{6}$
b.
$\frac{2}{5}\sqrt{6}=\sqrt{\frac{4}{25}.6}=\sqrt{\frac{24}{25}}< 1$
$\frac{7}{4}\sqrt{\frac{1}{3}}=\sqrt{\frac{49}{16}.\frac{1}{3}}=\sqrt{\frac{49}{48}}>1$
$\Rightarrow \frac{7}{4}\sqrt{\frac{1}{3}}> \frac{2}{5}\sqrt{6}$
Bài 10:
a. $\sqrt{5a^2}=\sqrt{5}.\sqrt{a^2}=\sqrt{5}|a|=-\sqrt{5}a$
b. $\sqrt{18a^2}=\sqrt{2(3a)^2}=\sqrt{2}.\sqrt{(3a)^2}$
$=\sqrt{2}|3a|=3a\sqrt{2}$
c.
\(\sqrt{-9b^3}=\sqrt{(3b)^2.(-b)}=\sqrt{(3b)^2}.\sqrt{-b}=|3b|\sqrt{-b}=-3b\sqrt{-b}\)
d.
\(\sqrt{24a^4b^8}=\sqrt{6(2a^2b^4)^2}=\sqrt{6}.\sqrt{(2a^2b^4)^2}=\sqrt{6}.|2a^2b^4|\)
\(=2a^2b^4\sqrt{6}\)