Question

simplify \\(\sqrt{112}\\).
step-by-step solution
step 1: what is the index on the radical?
the index on the radical is 2.
because the index is 2, write each factor of the radicand as the product of two factors, one of which is a perfect square.
the perfect squares are 1, 4, 9, 16, 25, ...
the largest perfect square factor of 112 is \\(\square\\)

Explanation:

Step1: List factors of 112

First, find the factors of 112. The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112.

Step2: Identify perfect square factors

From these factors, the perfect squares are 1, 4, 16. Now, among these, the largest one is 16. Because \(112\div16 = 7\), and 16 is a perfect square (\(4^2\)) and 7 is not a perfect square. So the largest perfect square factor of 112 is 16.

Answer:

16