Question

8 multiple choice 10 points \\(\sqrt{72}\\) \\(6\sqrt{2}\\) \\(3\sqrt{3}\\) \\(5\sqrt{5}\\) \\(4\sqrt{3}\\)

Explanation:

Step1: Factor 72 into perfect square and other

We know that \( 72 = 36\times2 \), where 36 is a perfect square (\( 6^2 \)). So, \( \sqrt{72}=\sqrt{36\times2} \).

Step2: Use square - root property \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (\( a\geq0,b\geq0 \))

According to the property of square roots \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (\( a = 36,b = 2 \)), we have \( \sqrt{36\times2}=\sqrt{36}\times\sqrt{2} \).
Since \( \sqrt{36} = 6 \), then \( \sqrt{36}\times\sqrt{2}=6\sqrt{2} \).

Answer:

\( 6\sqrt{2} \) (the option corresponding to \( 6\sqrt{2} \))