Question

simplify.
\sqrt{20y} + \sqrt{45y}
assume that the variable represents a positive real number.

Explanation:

Step1: Simplify each square root

Factor the radicands: \(20y = 4\times5y\) and \(45y = 9\times5y\). Then use the property \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (\(a\geq0,b\geq0\)).
\(\sqrt{20y}=\sqrt{4\times5y}=\sqrt{4}\cdot\sqrt{5y}=2\sqrt{5y}\)
\(\sqrt{45y}=\sqrt{9\times5y}=\sqrt{9}\cdot\sqrt{5y}=3\sqrt{5y}\)

Step2: Combine like terms

Now we have \(2\sqrt{5y}+3\sqrt{5y}\). Since the radicals are the same, we add the coefficients: \((2 + 3)\sqrt{5y}=5\sqrt{5y}\)

Answer:

\(5\sqrt{5y}\)