Question

7 multiple choice 10 points \\(\sqrt{50}\\) \\(5\sqrt{2}\\) 25 \\(2\sqrt{3}\\) \\(2\sqrt{5}\\)

Explanation:

Step1: Factor 50 into prime factors

We know that \( 50 = 25\times2 \), and \( 25 = 5^2 \). So we can rewrite \( \sqrt{50} \) as \( \sqrt{25\times2} \).

Step2: Use the property of square roots

The property of square roots states that \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (where \( a\geq0 \) and \( b\geq0 \)). Applying this property to \( \sqrt{25\times2} \), we get \( \sqrt{25}\times\sqrt{2} \).

Step3: Simplify \( \sqrt{25} \)

Since \( 5^2 = 25 \), \( \sqrt{25}=5 \). So \( \sqrt{25}\times\sqrt{2}=5\sqrt{2} \).

Answer:

A. \( 5\sqrt{2} \) (assuming the first option is labeled A, with the text \( 5\sqrt{2} \))