Question

5 multiple choice 10 points \\(\sqrt{32}\\) \\(2\sqrt{3}\\) \\(2\sqrt{4}\\) \\(2\sqrt{6}\\) \\(4\sqrt{2}\\)

Explanation:

Step1: Factor 32

We know that \( 32 = 16\times2 \), and \( 16 \) is a perfect square. So, \( \sqrt{32}=\sqrt{16\times2} \).

Step2: Use square - root property

According to the property of square roots \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (where \( a\geq0,b\geq0 \)), we have \( \sqrt{16\times2}=\sqrt{16}\times\sqrt{2} \).
Since \( \sqrt{16} = 4 \), then \( \sqrt{16}\times\sqrt{2}=4\sqrt{2} \).

Answer:

\( 4\sqrt{2} \) (the last option)