Question

What is the simplified form of the following expression? 3 sqrt 4x/5

Answer 1

The simplified form of the expression
`3 \sqrt(4x/5) \ is\ 6 \sqrt(5x) / 5`after performing the square root separately on the numerator and denominator, and then rationalizing the denominator.

Step-by-step explanation:

The expression given is
`3 \sqrt(4x/5)`. To simplify this expression, we observe that the square root of 4 is a perfect square and equals 2. The square root of the fraction can be taken by applying the square root to the numerator and the denominator separately. Therefore, we have:

`3 * \sqrt(4) * \sqrt(x) / \sqrt(5)`

Upon simplifying, we get:

`3 * 2 * \sqrt(x) / \sqrt(5)`

This simplifies further to:

`6 \sqrt(x) / \sqrt(5)`

However, it's not common to leave a square root in the denominator, so we can multiply both the numerator and the denominator by sqrt(5) to rationalize the denominator.

The final simplified form is:

`6 \sqrt(5x) / 5`