Question

how can the expression \\(\sqrt{112}\\) be correctly rewritten?

\\(4\sqrt{7}\\)
\\(\sqrt{4} \cdot \sqrt{7}\\)
\\(16\sqrt{7}\\)
\\(2\sqrt{56}\\)

Explanation:

Step1: Find the largest perfect square factor of 112

$$112 = 16 \times 7$$

Step2: Apply the product property of square roots

$$\sqrt{112} = \sqrt{16 \times 7} = \sqrt{16} \times \sqrt{7}$$

Step3: Simplify the square root of the perfect square

$$\sqrt{16} \times \sqrt{7} = 4\sqrt{7}$$

Answer:

\(4\sqrt{7}\)