IMathAS-libretexts

Radical Conjugates
Determine the Radical Conjugate of each of the following radical expressions, then find the product. The first one has been done for you.
Radical Expression	Radical Conjugate	Product
$\displaystyle {5}-\sqrt{{{2}}}$	$\displaystyle {5}+\sqrt{{{2}}}$	$\displaystyle {\left({5}-\sqrt{{{2}}}\right)}{\left({5}+\sqrt{{{2}}}\right)}$ $\displaystyle {25}+{5}\sqrt{{{2}}}-{5}\sqrt{{{2}}}-{\left(\sqrt{{{2}}}\right)}^{{2}}$ $\displaystyle {25}+{0}\sqrt{{{2}}}-{2}$ $\displaystyle {23}$
$\displaystyle {5}+\sqrt{{{11}}}$
$\displaystyle {7}-\sqrt{{{7}}}$
$\displaystyle \sqrt{{{5}}}+{9}$