Question

multiply. write your answer in simplest form.\\(sqrt{7} cdot sqrt{10}\\)

Explanation:

Step1: Recall the property of square roots

The product of square roots property states that \(\sqrt{a} \cdot \sqrt{b}=\sqrt{a\times b}\) for non - negative real numbers \(a\) and \(b\). Here, \(a = 7\) and \(b=10\).
So, \(\sqrt{7}\cdot\sqrt{10}=\sqrt{7\times10}\)

Step2: Calculate the product inside the square root

Calculate \(7\times10 = 70\). Since \(70\) does not have any perfect square factors (the factors of \(70\) are \(1,2,5,7,10,14,35,70\) and none of the non - 1 factors are perfect squares), \(\sqrt{70}\) is in simplest form.

Answer:

\(\sqrt{70}\)