Question

station 1 simplifying radicals
simplify the following radical:
\\(\sqrt{50}\\)
\\(6\sqrt{5}\\)
\\(12\sqrt{5}\\)
\\(5\sqrt{2}\\)
\\(7\sqrt{2}\\)
\\(12\sqrt{2}\\)
\\(6\sqrt{2}\\)

Explanation:

Step1: Factor the radicand

Factor 50 into a product of a perfect square and another number: \(50 = 25\times2\)
So, \(\sqrt{50}=\sqrt{25\times2}\)

Step2: Use the property of radicals

Use the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0,b\geq0\)):
\(\sqrt{25\times2}=\sqrt{25}\times\sqrt{2}\)

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

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

Answer:

\(5\sqrt{2}\) (corresponding to the option "5√2")