Chapter 8, Problem 1MCP

To determine

To simplify the given expression $\sqrt{50}·\sqrt{6}$.

Answer to Problem 1MCP

   $10\sqrt{3}$.

Explanation of Solution

Given:

We are given $\sqrt{50}·\sqrt{6}$.

Concept Used:

We will apply the multiplication rules of roots and simplify it to its lowest value.

And find the factors of the term to solve the roots.

Calculation:

We are given $\sqrt{50}·\sqrt{6}$ .

Now, we are simplifying the given expression, as,

   $\begin{array}{l}\sqrt{50}·\sqrt{6}\\ \text{We can simplify it as follows,}\\ =\sqrt{5\times 5\times 2}·\sqrt{6}\\ \text{{simplifying }\sqrt{6}\text{=}\sqrt{3\times 2}\text{}}\\ \text{{multiplying and solving the roots}}\\ =5\sqrt{2\times 3\times 2}\\ =5\times 2\sqrt{3}\\ =10\sqrt{3}\end{array}$

Thus, after simplification we have, $10\sqrt{3}$.