Question

question
express in simplest radical form.
\sqrt{112}

Explanation:

Step1: Factor 112 into prime factors

We need to find the largest perfect square factor of 112. First, factorize 112: $112 = 16\times7$, where 16 is a perfect square ($4^2$) and 7 is a prime number.

Step2: Apply the square root property

Using the property $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (for $a\geq0,b\geq0$), we can rewrite $\sqrt{112}$ as $\sqrt{16\times7}$. Then, $\sqrt{16\times7}=\sqrt{16}\times\sqrt{7}$. Since $\sqrt{16} = 4$, we get $4\sqrt{7}$.

Answer:

$4\sqrt{7}$