The problem asks us to reduce the radical $\sqrt{112}$. This means we want to simplify the square root of 112 by finding the largest perfect square that divides 112.

1. Problem Description

The problem asks us to reduce the radical $\sqrt{112}$. This means we want to simplify the square root of 112 by finding the largest perfect square that divides

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2. Solution Steps

We want to simplify $\sqrt{112}$.

First, we can find the prime factorization of 112:

$112 = 2 \times 56 = 2 \times 2 \times 28 = 2 \times 2 \times 2 \times 14 = 2 \times 2 \times 2 \times 2 \times 7 = 2^4 \times 7$.

Therefore, we have $\sqrt{112} = \sqrt{2^4 \times 7}$.

We can rewrite this as $\sqrt{2^4} \times \sqrt{7}$.

Since $2^4 = (2^2)^2 = 4^2 = 16$, we have $\sqrt{2^4} = \sqrt{16} = 4$.

So, $\sqrt{112} = 4\sqrt{7}$.

Formula used:

$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$

3. Final Answer

$4\sqrt{7}$