Question

select the correct answer.
solve the following.
\\(\sqrt{50} \times 3\sqrt{2} = ?\\)
\\(\circ\\) \\(6\sqrt{13}\\)
\\(\circ\\) \\(10\\)
\\(\circ\\) \\(30\\)
\\(\circ\\) \\(6\\)

Explanation:

Step1: Simplify \(\sqrt{50}\)

We know that \(50 = 25\times2\), and \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)). So \(\sqrt{50}=\sqrt{25\times2}=\sqrt{25}\times\sqrt{2}=5\sqrt{2}\).

Step2: Multiply the two radical expressions

Now we have \(\sqrt{50}\times3\sqrt{2}=5\sqrt{2}\times3\sqrt{2}\). Using the property of multiplication of radicals \(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\) and the commutative property of multiplication, we can rewrite this as \((5\times3)\times(\sqrt{2}\times\sqrt{2})\).

Step3: Calculate the product

First, \(5\times3 = 15\), and \(\sqrt{2}\times\sqrt{2}=\sqrt{2\times2}=\sqrt{4} = 2\). Then we multiply these results: \(15\times2=30\).

Answer:

30 (corresponding to the option "30")