The Product Rule indicates radical expression behavior. How did we do it? Well, in reality, there’s another property of radical expressions, which is the Product Rule of radical expressions. How do we simplify them? To tell you the truth, it’s quite simple. These numbers can’t even be expressed accurately with fractions of integers. Here are some examples:Īs you can see, the decimal part of these square roots won’t repeat nor terminate. Instead, the square root would be a number which decimal part would continue on endlessly without end and won’t show any repeating pattern. As radicands, imperfect squares don’t have an integer as its square root. Imperfect squares are the opposite of perfect squares. In that case, what if we want to simplify other radicals that don’t have a perfect square as its radicands? Simplifying Radicals Expressions with Imperfect Square Radicands 5, an integer, is the square root of 25). Recall that perfect squares are radicands that have an integer as its square root (e.g. If we want to simplify other radicals such as , and that has perfect square radicands-25 is also a perfect square, then the result would be 6, 7, and 4 respectively. In the example above, the simplification of is 5. Simplifying an expression meaning we are replacing it with an equivalent that is easier to digest and, if possible, shorter. If we want to simplify the expression above, we can do it like so: Since that is the case, we can hide the index part so it would be written like this: Radical expressions with the index of 2 are also referred to as square root. You can easily tell that the radicand of the expression equals to 25 while the index equals to 2. In this case, should you encounter a radical expression that is written like this: Meanwhile, √ is the radical symbol while n is the index. Looking at the radical expression above, we can determine that X is the radicandof the expression. Before we begin simplifying radical expressions, let’s recall the properties of them.
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