Sqrt(162) = sqrt(81*2) = sqrt(81)*sqrt(2) = 9*sqrt(2)
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It is easier to work with simplified radicals just as it is easier to work with simplified fractions. A fundamental rule for math is to simplify whenever possible, as much as possible.
radical 89 cannot be simplified.
A radical expression is an expression that involves a square root, cubic root, etc.
√105 in radical form is √105. It has no square factors and so cannot be simplified.
It will be radical(62). It cannot be simplified.