A) \(7+4\sqrt{3}\)
\(=4+4\sqrt{3}+3\)
\(=2^2+2\cdot2\cdot\sqrt{3}+\left(\sqrt{3}\right)^2\)
\(=\left(2+\sqrt{3}\right)^2\)
B) \(3\sqrt{2}+2\sqrt{3}\)
\(=\sqrt{3^2\cdot2}+\sqrt{2^2\cdot3}\)
\(=\sqrt{18}+\sqrt{12}\)
\(=\sqrt{6}\cdot\left(\sqrt{3}+\sqrt{2}\right)\)
C) \(\sqrt{45}-\sqrt{35}\)
\(=\sqrt{5\cdot9}-\sqrt{5\cdot7}\)
\(=\sqrt{5}\cdot\left(\sqrt{9}-\sqrt{7}\right)\)
\(=\sqrt{5}\left(3-\sqrt{7}\right)\)
D) \(x-y^2\)
\(=\left(\sqrt{x}\right)^2-y^2\)
\(=\left(\sqrt{x}+y\right)\left(\sqrt{x}-y\right)\)
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