Question

question
go step by step to reduce the radical.
\sqrt{112}
\sqrt{\square} \sqrt{\square}

Explanation:

Step1: Factor 112 into perfect square and another number

We know that \(112 = 16\times7\), where 16 is a perfect square. So we can rewrite \(\sqrt{112}\) as \(\sqrt{16\times7}\).

Step2: Use the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\))

Applying this property, \(\sqrt{16\times7}=\sqrt{16}\times\sqrt{7}\).

Step3: Simplify \(\sqrt{16}\)

Since \(4^2 = 16\), \(\sqrt{16}=4\). So now we have \(4\times\sqrt{7}=4\sqrt{7}\). But for the given form \(\sqrt{\square}\sqrt{\square}\), we just need to fill in the factors we used, which are 16 and 7.

Answer:

The first square is filled with 16 and the second square is filled with 7, so \(\sqrt{112}=\sqrt{16}\sqrt{7}\) (and further simplifies to \(4\sqrt{7}\) if needed, but for the given blanks, the values are 16 and 7).