Okay, I just need the steps for simplifying this type of radical:

5
--
3√2

thats all one problem.

thanks!

To simplify the expression (5/3)√2, follow these steps:

Step 1: Identify the perfect square factors
Check if there are any perfect square factors within the radical. In this case, the perfect square factor is 2.

Step 2: Group the factors
Write the expression as the product of two radicals. The first radical will contain the perfect square factor(s) identified in Step 1, and the second radical will contain the remaining factors. In this case, you'll have √2 * √(5/3).

Step 3: Simplify each radical separately
Simplify each radical separately if possible. The square root of 2 cannot be simplified further, but the square root of (5/3) can be simplified as follows:

Step 3.1: Simplify the fraction
To simplify the fraction (5/3), divide the numerator and denominator by their greatest common divisor (GCD), which is 1 in this case. So, (5/3) remains unchanged.

Step 3.2: Combine the simplified fraction with the square root
Now, combine the simplified fraction with the square root: √(5/3). At this point, the radical cannot be simplified further, so you have the simplified expression as √2 * √(5/3).

Step 4: Multiply the two radicals together
Finally, multiply the two radicals together: √2 * √(5/3) = √(2 * (5/3)) = √(10/3).

So, the simplified expression is √(10/3).