To simplify the given expression [tex]\(\sqrt{(11m)^2}\)[/tex], follow these steps:
1. Recognize the property of square roots and squares: [tex]\(\sqrt{a^2} = |a|\)[/tex]. This property tells us that the square root of a squared term is the absolute value of the original term.
2. Apply this property to our specific expression: [tex]\[\sqrt{(11m)^2}.\][/tex]
3. Here, [tex]\(a\)[/tex] in the property is [tex]\(11m\)[/tex], so: [tex]\[\sqrt{(11m)^2} = |11m|.\][/tex]
4. If we consider the fact that [tex]\(11\)[/tex] is a positive constant, we can factor the absolute value inside:
[tex]\[|11m| = 11|m|.\][/tex]
Thus, the simplified form of the given expression is:
[tex]\[ \sqrt{(11m)^2} = 11|m|. \][/tex]
Therefore, [tex]\(\sqrt{(11m)^2} = 11\)[/tex].
