Final answer:
To simplify √5x/x √ 20, simplify the two parts separately and then combine. We simplify √5x to √5 * √x / √x, and √20 to 2 * √5. Putting them together, we get 10.
Step-by-step explanation:
To simplify the expression √5x/x √ 20, we can start by simplifying each part separately.
First, we have √5x. The square root of 5x can be written as √5 * √x. Since we are dividing by x later, we can simplify it further to √5 * √x / √x.
Next, we simplify the second part, which is √20. The square root of 20 can be written as √4 * √5. And since √4 is 2, we have 2 * √5.
Now we can put both simplified parts together: (√5 * √x / √x) * (2 * √5). The √x in the numerator and denominator cancel out, leaving us with √5 * 2 * √5. Multiplying the numbers outside the square root gives us 2√5 * √5. Combining the two square roots, we get 2√5 * √5 = 2 * 5 = 10.