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\(=\sqrt{\left(3-\sqrt{3}\right)^2}-\sqrt{\left(2\sqrt{3}-3\right)^2}\)
\(=3-\sqrt{3}-2\sqrt{3}+3=6-3\sqrt{3}\)
`A=\sqrt{12-6\sqrt{3}}-\sqrt{21-12\sqrt{3}}`
`A=\sqrt{(\sqrt{3})^2-2.\sqrt{3}.2+3^2}-\sqrt{3^2-2.3.2\sqrt{3}+(2\sqrt{3})^2}`
`A=\sqrt{(\sqrt{3}-3)^2}-\sqrt{(3-2\sqrt{3})^2}`
`A=|\sqrt{3}-3|-|3-2\sqrt{3}|`
`A=(3-\sqrt{3})-(2\sqrt{3}-3)`
`A=3-\sqrt{3}-2\sqrt{2}+3`
`A=6-3\sqrt{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)\(\sqrt{xy}-4\sqrt{x}+3\sqrt{y}-12=\sqrt{x}\left(\sqrt{y}-4\right)+3\left(\sqrt{y}-4\right)=\left(\sqrt{x}+3\right)\left(\sqrt{y}-4\right)\)
\(\sqrt{12-6\sqrt{3}}+\sqrt{21-12\sqrt{3}}=\sqrt{\left(3-\sqrt{3}\right)^2}+\sqrt{\left(2\sqrt{3}-3\right)^2}=3-\sqrt{3}+2\sqrt{3}-3=\sqrt{3}\)
\(\sqrt{21}+\sqrt{3}+\sqrt{7}+1\)
\(=\sqrt{3}\left(\sqrt{7}+1\right)+\left(\sqrt{7}+1\right)\)
\(=\left(\sqrt{7}+1\right)\left(\sqrt{3}+1\right)\)
\(\sqrt{1-a}+\sqrt{1-a^2}\)
\(=\sqrt{1-a}+\sqrt{\left(1-a\right)\left(1+a\right)}\)
\(=\sqrt{1-a}\left(1+\sqrt{1+a}\right)\)
\(5\sqrt{14}-\sqrt{21}=\sqrt{7}\left(5\sqrt{2}-\sqrt{3}\right)\)
\(a=9-12\sqrt{3}+\left(2\sqrt{3}\right)^2\)
\(a=\left(3-2\sqrt{3}\right)^2\)