mat 117 week 5 DQ's 4 different explanation
mat 117 week 5 DQ's 4 different explanation
Popular in Course
verified elite notetaker
Popular in Department
This 6 page Study Guide was uploaded by needhelp Notetaker on Monday November 16, 2015. The Study Guide belongs to a course at a university taught by a professor in Fall. Since its upload, it has received 15 views.
Reviews for mat 117 week 5 DQ's 4 different explanation
Report this Material
What is Karma?
Karma is the currency of StudySoup.
You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!
Date Created: 11/16/15
Week 5 DQ 1 – Due Day 2 Please post a 150 300 word response to the following discussion question by clicking on Reply. Why is it important to simplify radical expressions before adding or subtracting? How is adding radical expressions similar to adding polynomial expressions? How is it different? Provide a radical expression for your classmates to simplify. Consider participating in the discussion by simplifying your classmates’ expressions. Detail what would have happened or if the expression was not simplified first. Explanation 1 It’s like adding fractions, and it’s better to first find a common denominator. Also, you may have two similar numbers and you cannot add them together until you simplify the radical expression. Examples are sqrt(8) + sqrt(18). At first look, you cannot add them together. However sqrt(8) simplifies to 2sqrt(2) and sqrt(18) simplifies to 3sqrt(2). You can now add them to get 5sqrt(2). Example: Good one to simplify is sqrt(96) which reduced down to 4 sqrt 6 You cannot directly add terms inside a radical, so you need to try to get the number inside the radical to be the same in each term. For example: sqrt(25) + sqrt(4), You can't just add the 25 and 4. Instead you simplify each one first: 5 + 2 = 7 The key is to add "like" terms. You can't add the coefficients of 3sqrt(6) and 4sqrt(2), but you can add the coefficients of 3sqrt(6) and 4sqrt(6). The difference here, though, is that you can simplify or change the numbers in the radicals. For example: sqrt(24) = sqrt(4*6) = 2sqrt(6). Performing operations like this can help find like terms. When adding or subtracting radical expressions the rule says the radical must be the same before you combine the numbers out in front. To make the radical expressions the same you must first simplify them by factoring. Note that sometimes you can't make them the same so you leave the way it is. Radical expressions are similar to adding polynomial expressions because you have a multiple of something to combine. For instance, 3*x really means you have 3 x's to add up x + x + x = 3*x same for 2*x. Therefore there is a total of 5 x's to add up or simply write 5*x. Same concept applies to radical expressions you have a multiple of something to add up. Simplify sqrt(24) + 4 sqrt(6) Explanation 2 When you simplify the radicals it is easier to add and subtract because you can combine the like terms. Before adding and or subtraction radicals it is important to use the order of operation to analyze the expressions. In radicals if the expressions are different or not alike then you would have to find the difference by adding the opposites. With polynomials you can also add or subtract terms if they are like terms. They also differ because in radical expression like terms are determined by the value that is inside the root; in polynomials the terms are determined by the variables and their powers. When simplifying a radical expressing it can involve variables as well as numbers and variables can be broken down just like numbers can. Below are a few examples that I ask the class to solve Please simply the square root of 24 Please simply the square root of 24/7 Please simply the square root of 14x Explanation 3 It is important to simplify radical expressions before adding or subtracting because they need to be in the simplest form. They have to have the same number and in order to find that you must make sure they are simplified. It is similar to adding polynomial expressions because in both instances, you can only add like terms. However you are not dealing with exponents with radical expressions, you are dealing with square roots of a number instead. Exponents and square roots change the type of problem completely and determine a certain answer. Either way, you have to double check your work and make sure before you finish the problem that all problems are in their simplest form. Please try and solve: 3 square root of 6 + 2 square root of 12 Remember to simplify and double check. If they are not the same, you cannot add them together. Explanation 4 It is important to simplify radical expressions first because through this process we are able to collect like terms (as long as the index and radicand are the same) in order to find the square roots of the expression. This process is similar to working with polynomial expressions in that there, we are combining like terms and exponents. Factoring is used in both processes as well in order to find like terms. Problem 4+√54 +√24 Week 5 DQ 2 – Due Day 4 Please post a 150 300 word response to the following discussion question by clicking on Reply. Review section 10.2 (p. 692) of your text. Describe two laws of exponents and provide an example illustrating each law. Explain how to simplify your expression. How do the laws work with rational exponents? Provide the class with a third expression to simplify that includes rational (fractional) exponents. Consider responding to classmates who have chosen laws different from the ones you selected. Ask clarifying questions of your classmates to make sure you understand the laws. Practice simplifying your classmates’ expressions. Explanation 1 The laws of exponents in our text are broken down into five different categories, the two I will explain are multiplying and dividing. When multiply, exponents can be added as long as the bases are the same. When dividing, the exponents can be subtracted if the bases are the same. In order to simply the radical expression needs to be converted into an exponential expression, then we would use math and then simplify by using the laws of exponents, the last step would be to convert it back into the radical notation when that step applies. The rules of exponents are still valid for rational exponents, it is just easier to simplify the radical than using rational exponents because of how it is simplified. Another important factor that I learned was when a radical expression is given it can be converted into a fractional power. (6 1/4)/(6 1/2) Explanation 2 Two laws for dealing with exponents are with multiplying and dividing. In multiplying, the exponents can be added if the bases are the same, example; m n m+n a x a = a 4 3 4+3 65y x 65y = 65y 7 = 65y When dividing, we can subtract the exponents if the bases are the same, example; am ÷ a = a m-n 65y ÷ 65y = 65y 4-3 = 65y These same laws apply with rational exponents, multiplication example; 65y 2/4x 65y 1/= Division example; 2/4 65y 65y 1/4= Explanation 3 The two laws of exponents I will describe are multiplying exponents and dividing exponents. In my opinion, both of these techniques are easy to remember and easy to operate through. When multiplying exponents, all you have to do is add the exponents that appear throughout the equation. For example, 2^2/7 * 2^3/7 = 2^5/7. When dividing exponents, the exact opposite has to occur. You must subtract exponents when dividing numbers containing exponents. For example, 3^3/5 3^1.5= 3^2/5 Two things that you must remember when performing these operations is that if there is not already a common denominator, you must find one, and if simplified exponents are negative, you must put them in positive form. As stated above, the laws are the same when dealing with fractional or nonfractional exponents. Just remember the simple rules like keeping bases the same and answering exponent in positive form as well as solving with common denominators when necessary. Problem for the class to solve: 10^6/7 10^2/7 Explanation 4 Two laws of exponents for any real number a and any rational exponent m and n. Power Rule: To raise a power to a power, you multiply exponents, such as (am)n = amn . For example, (82/5)5/2 = 82/5·5/2 = 810/10 = 81 = 8. For this expression, I simply multiplied exponents together and simplified. Raising a Product to a Power Rule: To raise a product to a power, you raise each factor to the power, such as (ab)m = ambm. For example, (a²b)1/2 = a2·1/2b1/2 = a1b1/2 = ab1/2. In this example, I raised each factor (a and b) to the power (1/2), multiplied exponents, and simplified. With rational exponents, the laws of exponents work the same as with integer exponents. The only difference is that you are using fractions instead of integers. Expression to simplify that includes rational exponents: 24va4b2 , or the 24th root of a4b2
Are you sure you want to buy this material for
You're already Subscribed!
Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'