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 we can rewrite \(\sqrt{300}\) as \(\sqrt{100\times3}\).

Step2: Apply square - root property

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

Step3: Simplify \(\sqrt{100}\)

Since \(10^2 = 100\), \(\sqrt{100}=10\). So \(\sqrt{300}=10\sqrt{3}\). But for the given form \(\sqrt{\square}\sqrt{\square}\), we fill in the blanks with \(100\) and \(3\) respectively.

Answer:

The first blank is \(100\) and the second blank is \(3\), so \(\sqrt{300}=\sqrt{100}\sqrt{3}\)