Question

question
go step by step to reduce the radical.
\\(\sqrt{216}\\)
\\(\sqrt{\square}\\) \\(\sqrt{\square}\\)

Explanation:

Step1: Factor 216 into perfect square and other

We know that \(216 = 36\times6\), where \(36\) is a perfect square. So we can rewrite \(\sqrt{216}\) as \(\sqrt{36\times6}\).

Step2: Use property of square roots

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\)), we get \(\sqrt{36\times6}=\sqrt{36}\times\sqrt{6}\).

Step3: Simplify \(\sqrt{36}\)

Since \(6^2 = 36\), \(\sqrt{36}=6\). So the simplified form is \(6\sqrt{6}\). But for the first step of breaking into two square roots, we have \(\sqrt{216}=\sqrt{36}\sqrt{6}\)

Answer:

The two numbers in the boxes are \(36\) and \(6\) (or \(6\) and \(36\)), and the simplified radical is \(6\sqrt{6}\)