Question

go step by step to reduce the radical. \\(\sqrt{180}\\) \\(\sqrt{\square}\sqrt{\square}\\)

Explanation:

Step1: Factor 180 into perfect square and other

We know that \(180 = 36\times5\), where \(36\) is a perfect square (\(6^2\)).
So, \(\sqrt{180}=\sqrt{36\times5}\)

Step2: Apply square - root property

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\)), we get \(\sqrt{36\times5}=\sqrt{36}\times\sqrt{5}\)

Answer:

The two numbers in the boxes are \(36\) and \(5\) (or \(5\) and \(36\)), so \(\sqrt{180}=\sqrt{36}\sqrt{5}\) (or \(\sqrt{5}\sqrt{36}\))