Question

simplify \\(\sqrt{9y^2}\\)

Explanation:

Step1: Simplify the square root of 9

The square root of 9 is 3, since \(3\times3 = 9\). So we can rewrite \(\sqrt{9y^{2}}\) as \(\sqrt{9}\times\sqrt{y^{2}}\), and \(\sqrt{9}=3\).

Step2: Simplify the square root of \(y^{2}\)

The square root of \(y^{2}\) is \(|y|\) (the absolute value of \(y\)) because \(\sqrt{a^{2}}=|a|\) for any real number \(a\). However, if we assume \(y\) is non - negative (a common assumption in some basic algebra problems unless stated otherwise), then \(\sqrt{y^{2}} = y\).
Combining the two results, \(\sqrt{9y^{2}}=\sqrt{9}\times\sqrt{y^{2}} = 3y\) (assuming \(y\geq0\)).

Answer:

\(3y\) (or \(3|y|\) if we consider all real values of \(y\))