Question

6.1 simplifying radical expressions and applying the pythagorean theorem, converse, and solving right triangles pretest

question 2
simplify.
\\(\sqrt{112}\\)

Explanation:

⚡ Using what you learned: simplifying radical expressions

Step 1: Find the largest perfect square factor

Identify the largest perfect square that divides evenly into \(112\).

$$ 112 = 16 \times 7 $$

Step 2: Apply the product property of radicals

Split the radical using the property \(\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}\).

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

Step 3: Simplify

Simplify the square root of the perfect square.

$$ 4\sqrt{7} $$

Answer:

\(4\sqrt{7}\)