Express the following mixed radicals as entire radicals
5x√6x
To express 5x√6x as an entire radical, we need to simplify the expression using the rules of radicals:
First, we can simplify the square root term √6x by breaking it down into its factors:
√6x = √(2 * 3 * x) = √2 * √(3x) = √2 * √3x
Now, we can rewrite the expression as:
5x√6x = 5x(√2 * √3x)
To further simplify this expression, we can distribute the 5x to both terms inside the parentheses:
5x(√2 * √3x) = 5x√2 * 5x√3x = 5 * x * √2 * 5 * √3x = 25x√2√3x
Finally, since √2 is a rational number, we can further simplify the expression as:
25x√2√3x = 25x√(2 * 3 * x) = 25x√(6x)
Therefore, the entire radical expression for 5x√6x is 25x√(6x).