Simplifying Radicals

In this section, we learn about Simplifying Radicals, Multiplying Radicals, and Dividing Radicals. We begin by learning about the product rule for radicals. The product of two square roots is the square root of the product. This means we can take something like the square root of 20 and make it into the square root of 4 • the square root of 5. Since the square root of 4 is the same as 2, we just replace it with a 2. This gives us 2 • the square root of 5. This is the basic idea behind simplifying. We always prefer a rational number such as 2 to something such as the square root of 4. So when we look at something like the square root of 8, we can break it down to the square root of 4 • the square root of 2. We replace the square root of 4 with 2 and end up with 2 • the square root of 2. The quotient rule for radicals is very similar; the square root of a quotient is the quotient of the square roots. The difference here is we have to guard against division by zero since it is undefined.