Question

question
go step by step to reduce the radical.
\sqrt{300}
\sqrt{\square} \sqrt{\square}

Explanation:

Step1: Factor 300 into perfect square and other

We know that \(300 = 100\times3\), where \(100\) is a perfect square. So, \(\sqrt{300}=\sqrt{100\times3}\).

Step2: Apply square - root property

Using the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\)), we can rewrite \(\sqrt{100\times3}\) as \(\sqrt{100}\times\sqrt{3}\).

Answer:

The two numbers in the boxes are \(100\) and \(3\) respectively, and \(\sqrt{300}=\sqrt{100}\sqrt{3} = 10\sqrt{3}\) (if we further simplify \(\sqrt{100}\)). But for the form \(\sqrt{\square}\sqrt{\square}\), the answer is \(\sqrt{100}\sqrt{3}\)