Question

simplify (sqrt{9y^2})

Explanation:

Step1: Apply square - root property

We know that for non - negative real numbers \(a\) and \(b\), \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\). So, we can split \(\sqrt{9y^{2}}\) as \(\sqrt{9}\times\sqrt{y^{2}}\).

Step2: Simplify each square - root

We know that \(\sqrt{9} = 3\) because \(3\times3=9\). And for \(\sqrt{y^{2}}\), by the property of square - roots, \(\sqrt{x^{2}}=\vert x\vert\), but if we assume \(y\) is a non - negative real number (a common assumption when simplifying radical expressions without a domain specified otherwise), then \(\sqrt{y^{2}}=y\).
So, \(\sqrt{9}\times\sqrt{y^{2}} = 3\times y=3y\).

Answer:

\(3y\)