Question

2 multiple choice 10 points \\(\sqrt{63}\\) \\(3\sqrt{7}\\) \\(5\sqrt{7}\\) \\(2\sqrt{7}\\) \\(7\sqrt{3}\\)

Explanation:

Step1: Factor 63

Factor 63 into prime factors: \( 63 = 9\times7 \)

Step2: Simplify the square root

Using the property \( \sqrt{ab} = \sqrt{a}\times\sqrt{b} \) (where \( a\geq0, b\geq0 \)), we have \( \sqrt{63} = \sqrt{9\times7} = \sqrt{9}\times\sqrt{7} \)
Since \( \sqrt{9} = 3 \), then \( \sqrt{63} = 3\sqrt{7} \)

Answer:

A. \( 3\sqrt{7} \) (assuming the first option is labeled A, with the text \( 3\sqrt{7} \))