Question

lesson: simplifying radicals
simplify: √28
= √□ · √□
= □√□

Explanation:

Step1: Factor 28 into perfect square and other

We know that \( 28 = 4\times7 \), and \( 4 \) is a perfect square. So, \( \sqrt{28}=\sqrt{4\times7} \). By the property of square roots \( \sqrt{ab}=\sqrt{a}\cdot\sqrt{b} \) (where \( a = 4 \), \( b=7 \)), we get \( \sqrt{28}=\sqrt{4}\cdot\sqrt{7} \).

Step2: Simplify \( \sqrt{4} \)

Since \( \sqrt{4} = 2 \), we substitute this back into the expression. So \( \sqrt{4}\cdot\sqrt{7}=2\sqrt{7} \).

Answer:

First two boxes: \( 4 \), \( 7 \); Last two boxes: \( 2 \), \( 7 \) (So the filled steps are \( \sqrt{28}=\sqrt{4}\cdot\sqrt{7}=2\sqrt{7} \))