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Lời giải:
a.
\(5+\sqrt{3}+5\sqrt{3}+3=(5+5\sqrt{3})+(\sqrt{3}+3)\)
\(=5(1+\sqrt{3})+\sqrt{3}(1+\sqrt{3})=(1+\sqrt{3})(5+\sqrt{3})\)
b.
\(\sqrt{x}+\sqrt{y}+\sqrt{xy}+1=(\sqrt{x}+\sqrt{xy})+(\sqrt{y}+1)\)
\(=\sqrt{x}(1+\sqrt{y})+(\sqrt{y}+1)=(\sqrt{y}+1)(\sqrt{x}+1)\)
c.
$x-4\sqrt{x}+3=(x-\sqrt{x})-(3\sqrt{x}-3)$
$=\sqrt{x}(\sqrt{x}-1)-3(\sqrt{x}-1)$
$=(\sqrt{x}-1)(\sqrt{x}-3)$
a)\(a-5\sqrt{a}=\sqrt{a}\left(\sqrt{a}-5\right)\)
b)\(a-7=\left(\sqrt{a}-\sqrt{7}\right)\left(\sqrt{a}+\sqrt{7}\right)\)
c)\(a+4\sqrt{a}+4=\left(\sqrt{a}+2\right)^2\)
d)\(\sqrt{xy}-4\sqrt{x}+3\sqrt{y}-12=\sqrt{x}\left(\sqrt{y}-4\right)+3\left(\sqrt{y}-4\right)=\left(\sqrt{x}+3\right)\left(\sqrt{y}-4\right)\)
b, \(a+b+2\sqrt{a.b}=\sqrt{a^2}+\sqrt{b^2}+2\sqrt{ab}=\left(\sqrt{a}+\sqrt{b}\right)^2\) ( Vì a, b >= 0 )
c, \(a+b-2\sqrt{a.b}=\sqrt{a^2}+\sqrt{b^2}-2\sqrt{ab}=\left(\sqrt{a}-\sqrt{b}\right)^2\)( Vì a, b >= 0 )
\(x-5\)
\(=\left(\sqrt{x}\right)^2-\left(\sqrt{5}\right)^2\)
\(=\left(\sqrt{x}-\sqrt{5}\right)\left(\sqrt{x}+\sqrt{5}\right)\)
a)
\(7\sqrt{12}+\frac{1}{3}\sqrt{27}-\sqrt{75}\)
\(=14\sqrt{3}+\sqrt{3}-5\sqrt{3}\)
\(=10\sqrt{3}\)
b)
\(\left(2\sqrt{20}+\sqrt{125}-3\sqrt{80}\right):5\)
\(=\left(4\sqrt{5}+5\sqrt{5}-12\sqrt{5}\right):5\)
\(=-3\sqrt{5}:5\)
\(=\frac{-3\sqrt{5}}{5}\)
c)
\(3\sqrt{12a}-5\sqrt{3a}+\sqrt{48a}\)
\(=6\sqrt{3a}-5\sqrt{3a}+4\sqrt{3a}\)
\(=5\sqrt{3a}\)
tks