![]() In case you are wondering, we multiply the equation with to rationalize the denominator. Look at the process and you’ll see that it only takes simple calculations. This time, the road we took is longer but it’s actually not that different. Let’s take a look at a more difficult problem: Voila! The rather convoluted expression of is easily solved using the rule. Let’s sharpen our calculation skill with a couple of examples: Well, looking simply at the definition will hardly do any good. That is, the division between two or more radical expressions with the same index-let’s say n-is always equal to the radical expression of the quotient between the previous radicands, with the index of n. The Quotient Rule denotes the property of radicals differently. ![]() The only difference is that we split apart the 4s into two 2s for each, giving it more explanations as to how the radical expressions with the radicands of 4 are simplified. The problem is similar to the one before. Once you’ve done, take a look at this one. Can you find the different methods of solving it? Try it! ![]() ![]() There are multiple ways of simplifying . Afterward, we put each of the numbers into its own radical expressions, then grouped them again into a more manageable form, which is . Let’s deepen our understanding with a few more examples.įrom the equation above, we separate the radicand (72) into three different numbers (4, 9, and 2). With this rule, we can more easily simplify radical expressions that are seemingly complicated like before. To understand it better, consider the equation below: That is, if two or more radical expressions with the same index-let’s say n-are multiplied, the result would be equal to the radical expression of the product between the previous radicands, with the index of n. 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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