Multiplying Radicals:

Multiplying radicals in math can seem tricky at first, but once you understand the process, it becomes much easier. I find it easiest to think of it like typical multiplication with an extra set of numbers.

Step 1: Multiply the Coefficients

The first thing I do is multiply the coefficients (the numbers in front of the radicals). For example, if I have 3√2 and 4√5, I start by multiplying 3 and 4, which gives me 12.

Step 2: Multiply the Radicands

Next, I multiply the radicands (the numbers under the radical sign). Using the same example, I multiply 2 and 5, which gives me 10. So, 3√2 × 4√5 becomes 12√10.

Step 3: Simplify

After multiplying, I simplify the result if possible. In the example above, 12√10 is already in its simplest form. However, if the radicand can be simplified, I do so. For instance, if I end up with √18, I simplify it to 3√2 (since √18 = √(9×2) = 3√2). Both ways are equivalent, but it’s good to simplify as far as logically possible.

Example:

1. Example 1: Simple Multiplication2​√3 x 4√5

   First, I multiply the coefficients:

   2×4=8
   Then, I multiply the radicands:

   √3 x √5 = √15
   ​Which means,

   2√3 x 4√5​ = 8√15