Question

multiply. write your answer in simplest form. \\(sqrt{35} cdot sqrt{10}\\)

Explanation:

Step1: Use property of square roots

The property of square roots states that \(\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\) for non - negative real numbers \(a\) and \(b\). So, for \(\sqrt{35}\cdot\sqrt{10}\), we can rewrite it as \(\sqrt{35\times10}\).

Step2: Simplify the product inside the square root

Calculate \(35\times10 = 350\). So now we have \(\sqrt{350}\).

Step3: Factor the number inside the square root

Factor \(350\) into its prime factors: \(350=25\times14\), and \(25 = 5^{2}\). So \(\sqrt{350}=\sqrt{25\times14}\).

Step4: Use the square root property again

Using the property \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (where \(a = 25\) and \(b = 14\) and \(a\) is a perfect square), we get \(\sqrt{25\times14}=\sqrt{25}\cdot\sqrt{14}\). Since \(\sqrt{25} = 5\), the expression simplifies to \(5\sqrt{14}\).

Answer:

\(5\sqrt{14}\)