Question

multiply. write your answer in simplest form.\\(\sqrt{7} \cdot \sqrt{30}\\)

Explanation:

Step1: Use the 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 \(\sqrt{7}\cdot\sqrt{30}\), we can apply this property.
\(\sqrt{7}\cdot\sqrt{30}=\sqrt{7\times30}\)

Step2: Calculate the product inside the square root

Calculate \(7\times30 = 210\). So we have \(\sqrt{210}\). Since \(210 = 2\times3\times5\times7\) and there are no perfect square factors (other than 1) in 210, \(\sqrt{210}\) is in its simplest form.

Answer:

\(\sqrt{210}\)