Adding Radicals

Adding radicals in math is actually a lot more simple than I originally thought. Radicals (or roots) are expressions that involve the root of a number. The most common type is the square root, but there are also cube roots, fourth roots, and so on. Here’s how I approach adding radicals:

Step 1: Simplify the Radicals

The first thing I do is simplify the radicals. Simplifying a radical means breaking it down into its simplest form. For example, I take √50 and simplify it to 5√2 because you can pull out a five. This is because when factored, 50 breaks down into the prime factors: 5, 5, 2. and as it’s a square root, you need two of the same number to pull them out.

Step 2: Ensure Like Radicals

Next, I check to make sure the radicals are the same, which means they have the same radicand (the number under the radical sign) and the same degree of the root (square, cube, fourth, etc). For instance, 3√2 and 5√2 are like radicals because they both have the radicand 2 and are both square roots. On the other hand, √2 and √3 are not like radicals and can’t be added directly.

Step 3: Add the Coefficients

Once I have like radicals, I add them by simply adding their coefficients (the numbers in front of the radicals) while keeping the radical part the same. For example: 3√2 + 5√2 = (3 + 5)√2 = 8√2. Overall pretty simple, but also very important to remember.

Example Problem

1. Example 1: Simple Addition2√3 + 4√3​
   Since the radicals are the same, I just add the coefficients:2 + 4 = 6So,

   2√3 + 4√3​ = 6√3